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Prove that√2 is rational

Posted by Mohd Arman 2 years, 1 month ago

CBSE > Class 10 > Mathematics

2 answers

Ayush Singh 2 years, 1 month ago

√2 = p/q, where 'p' and 'q' are integers, q ≠ 0 and p, q have no common factors (except 1).

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Prakhar Sharma 2 years, 1 month ago

Let us assume on the contrary that 2 is a rational number. Then, there exist positive integers a and b such that 2 = b a where, a and b, are co-prime i.e. their HCF is 1 ⇒( 2 ) 2 =( b a ) 2 ⇒2= b 2 a 2 ⇒2b 2 =a 2 ⇒2∣a 2 [∵2∣2b 2 and 2b 2 =a 2 ] ⇒2∣a...(i) ⇒a=2c for some integer c ⇒a 2 =4c 2 ⇒2b 2 =4c 2 [∵2b 2 =a 2 ] ⇒b 2 =2c 2 ⇒2∣b 2 [∵2∣2c 2 ] ⇒2∣b...(ii) From (i) and (ii), we obtain that 2 is a common factor of a and b. But, this contradicts the fact that a and b have no common factor other than 1. This means that our supposition is wrong. Hence, 2 is an irrational number.

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ANSWER

What is 2-1

Posted by Hasithekshini Busala 2 years, 1 month ago

CBSE > Class 10 > Mathematics

5 answers

Chinmayi P P 2 years, 1 month ago

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Rahul Singh Bisht 2 years, 1 month ago

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Ayush Singh 2 years, 1 month ago

😌0

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Soham Singh 2 years, 1 month ago

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Omya Aryan 2 years, 1 month ago

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Construct a ∆ PQR in which PQ=5.2cm , PR=6.0 cm and QPR=55°

Posted by Ashi Ashi 2 years, 1 month ago

CBSE > Class 10 > Mathematics

1 answers

Omya Aryan 2 years, 1 month ago

Construction is not in syllabus

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Rainwater harvesting system is a technology that collects and stores rainwater for human use Anup decided to do rainwater harvesting he collected rainwater in underground tank at the rate of 30 cm cube per second what will be the equation formed.

Posted by Sapna N 2 years, 1 month ago

CBSE > Class 10 > Mathematics

1 answers

Rahul Singh Bisht 2 years, 1 month ago

30x

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an= (-1)n ×2n

Posted by Pavani Chugh 2 years, 1 month ago

CBSE > Class 10 > Mathematics

0 answers

ANSWER

In figure, if the area of DXYZ is 32 cm , then find the area of the quadrilateral PYZQ.

Posted by Aayuj Patel 2 years, 1 month ago

CBSE > Class 10 > Mathematics

0 answers

ANSWER

What is an composite number

Posted by Adesh Tomar 2 years, 1 month ago

CBSE > Class 10 > Mathematics

3 answers

Anjali Nagar 2 years, 1 month ago

Which have more than 2 factor

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Ashutosh Sharma 2 years, 1 month ago

Factor more than 2

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Omya Aryan 2 years, 1 month ago

The number which has more than 2 factors is factors is known as composite number. OR numbers other than prime number is known as composite number.

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Prove that : tan sec tan sec 1 1 θ θ θ θ − − + − = sec t θ θ

Posted by Hema Malini 2 years, 1 month ago

CBSE > Class 10 > Mathematics

0 answers

ANSWER

show me 3.3 full ex

Posted by Shiv Kumar 2 years, 1 month ago

CBSE > Class 10 > Mathematics

0 answers

ANSWER

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Posted by Palak Singhal 2 years, 1 month ago

CBSE > Class 10 > Mathematics

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Proof that 5-2√3 is a irrational no

Posted by Bhumi Chaudhary 2 years, 1 month ago

CBSE > Class 10 > Mathematics

0 answers

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Find the zeroes of x²+7x+6 and verify the relationship between zeroes and different

Posted by Aryan Singh 2 years, 1 month ago

CBSE > Class 10 > Mathematics

3 answers

Alok Kumar 2 years, 1 month ago

X²+7x+6 X²+6x+x+6 X(x+6)+1(x+6) (X+1)(x+6) Zeros of the polynomial X+1=0 X=-1 X+6=o X=-6 Sum of zeros Alpha + beta =-b\a -6+(-1)=-7\1 7 =7 Alpha ×beta =c\a -6×(-1). =6\1 6. =6 PROVED

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Omya Aryan 2 years, 1 month ago

Sum of zeros = -b/a = -7……Product of zeros = c/a = 6

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Omya Aryan 2 years, 1 month ago

x²+7x+6……x²+6x+1x+6……x(x+6)+1(x+6)……(x+1)(x+6)……x=-1 or x=-6

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Posted by Nitesh Yadav 2 years, 1 month ago

CBSE > Class 10 > Mathematics

0 answers

ANSWER

Number of Prmie Factors in 3233

Posted by Rajeev Rajpoot 2 years, 1 month ago

CBSE > Class 10 > Mathematics

2 answers

Preeti Dabral 2 years, 1 month ago

Prime Factors of 3233 are: 53, 61.

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Rajeev Rajpoot 2 years, 1 month ago

What is Reflection of light

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If P = 5-2√6 . Find the value of (1-p)^2 / p^2

Posted by Gauri Basetiya 2 years, 1 month ago

CBSE > Class 10 > Mathematics

0 answers

ANSWER

Show that 1/2 and -3/2 are the zeroes of the polynomial 4x²+4x-3 and verify the relationship between zeroes and coefficients of polynomial

Posted by Anilkumar P S Anilkumar 2 years, 1 month ago

CBSE > Class 10 > Mathematics

1 answers

Preeti Dabral 2 years, 1 month ago

f(x) = 4x² + 4x - 3
$\Rightarrow \quad f \left( \frac { 1 } { 2 } \right) = 4 \left( \frac { 1 } { 4 } \right) + 4 \left( \frac { 1 } { 2 } \right) - 3$
= 1 + 2 - 3 = 0
and $f \left( - \frac { 3 } { 2 } \right) = 4 \left( \frac { 9 } { 4 } \right) + 4 \left( - \frac { 3 } { 2 } \right) - 3$
= 9 - 6 - 3 = 0
$\therefore \frac { 1 } { 2 } , - \frac { 3 } { 2 }$ are zeroes of polynomial 4x² + 4x - 3.
Sum of zeroes = $\frac { 1 } { 2 } - \frac { 3 } { 2 } = - 1 = \frac { - 4 } { 4 }$
$= - \frac { \text { Coefficient of } x } { \text { Coefficient of } x ^ { 2 } }$
Product of zeroes = $\left( \frac { 1 } { 2 } \right) \left( - \frac { 3 } { 2 } \right) = \frac { - 3 } { 4 }$
$= \frac { \text { Constant term } } { \text { Coefficient of } x ^ { 2 } }$
Verified.

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Find the Next four term of the series 4,5,30,61

Posted by Ali Ahamad Khan 2 years, 1 month ago

CBSE > Class 10 > Mathematics

1 answers

Avinash Tripathi 2 years, 1 month ago

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Kon sa chapter ki practice karle ki pass ho jaye

Posted by Aman Khan 2 years, 1 month ago

CBSE > Class 10 > Mathematics

2 answers

Anvesha Sahay 2 years, 1 month ago

All chapters are important we can't choose any particular chapter to do practice of it and get passed easily.

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Nishant Singh 2 years, 1 month ago

Statics

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ANSWER

Prove that 2\√2 is irrational

Posted by Akhilesh Shankhdhar 2 years, 1 month ago

CBSE > Class 10 > Mathematics

1 answers

Akhilesh Shankhdhar 2 years, 1 month ago

Prove टू अपऑन अंडर रूट 2 इज irrational

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ANSWER

Sin30ki value

Posted by Khursheed Alam 2 years, 1 month ago

CBSE > Class 10 > Mathematics

5 answers

Raunak Yadav 2 years, 1 month ago

√1/2

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Deepak Sharma 2 years, 1 month ago

½ is the value of sin30°

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Anushka Sharma 2 years, 1 month ago

1/2 is the value of sin30°

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Varsha Chauhan 2 years, 1 month ago

0.5

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Hrishikesh Debnath 2 years, 1 month ago

One and half

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Find the value of sin30×cos60+cos30×sin60

Posted by Chinmayi P P 2 years, 1 month ago

CBSE > Class 10 > Mathematics

2 answers

Khursheed Alam 2 years, 1 month ago

Ajns

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Shreyash Kumar Jaiswal 2 years, 1 month ago

1/2 * 1/2 + √3/2 * √3/2 1/4 +3/4 4/4 1

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ANSWER

sin 45+cos 90=?

Posted by Chinmayi P P 2 years, 1 month ago

CBSE > Class 10 > Mathematics

2 answers

Sarika Joshi 2 years, 1 month ago

1/√2 + 0 is 1/√2

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Shreyash Kumar Jaiswal 2 years, 1 month ago

1/2 + 1 = 1/2+2/2 = 3/2

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prove that root 2 irrational number

Posted by Satyam Gupta 2 years, 1 month ago

CBSE > Class 10 > Mathematics

2 answers

Paritosh Rajput 2 years, 1 month ago

Prove

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Navkirat Kaur 2 years, 1 month ago

Let √2 is rational √2=a/b Where a and b are integers and b is not equal to 0 Rational is not equal to Irrational Our assumption is wrong √2 is irrational

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ANSWER

Explain 17*15*3*2+2*11 as a composte number

Posted by Tharun Nayak 2 years, 1 month ago

CBSE > Class 10 > Mathematics

2 answers

Preeti Dabral 2 years, 1 month ago

17×5×11×3×2+2×11=17×5×3×22+22

=22(17×5×3+1)
=22(255+1)=2×11×256 -----(i)

Equation (i) is divisible by 2, 11 and 256, so it has more than 2 prime factors.

∴ (17×5×11×3×2+2×11) is a composite number.

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Payal Kumari Kushwaha 2 years, 1 month ago

Don't post personal information, mobile numbers and other details.
Don't use this platform for chatting, social networking and making friends. This platform is meant only for asking subject specific and study related questions.
Be nice and polite and avoid rude and abusive language. Avoid inappropriate language and attention, vulgar terms and anything sexually suggestive. Avoid harassment and bullying.
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17*15*3+2*11

Posted by Tharun Nayak 2 years, 1 month ago

CBSE > Class 10 > Mathematics

1 answers

Preeti Dabral 2 years, 1 month ago

787

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From a solid cylinder of hieght 14 cm and base the diameter 7 cm . Two equal conical holes each of radius 2.1 cm and height 4 cm are cut out Find the volume and surface area of the remaining solid

Posted by Afiya Afiya 2 years, 1 month ago

CBSE > Class 10 > Mathematics

1 answers

Preeti Dabral 2 years, 1 month ago

Height of the cylinder (h) = 14 cm,
Base diameter = 7 cm
$\Rightarrow$ Radius of the base of the cylinder (r) = 3.5 cm
Volume of the cylinder = $\pi r ^ { 2 } h$
= $\frac { 22 } { 7 } \times 3.5 \times 3.5 \times 14$
= 22 $\times$ 3.5 $\times$ 3.5 $\times$ 14
= 539 cm³
Radius of the conical holes (r1) = 2.1 cm,
Height of the conical holes (h1) = 4 cm,
volume of the conical hole $= \frac { 1 } { 3 } \pi r _ { 1 } ^ { 2 } h _ { 1 }$
$= \frac { 1 } { 3 } \times \frac { 22 } { 7 } \times 2.1 \times 2.1 \times 4$
= 18.48 cm³
Volume of the two conical hole = 2 $\times$ 18.48
= 36.96 cm³
Volume of the remaining solid = Volume of the cylinder - Volume of two conical hole
= 539 - 36.96
= 502.04 cm³

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ANSWER

What is imperical relationship ?.

Posted by ._Nishant _. 2 years, 2 months ago

CBSE > Class 10 > Mathematics

2 answers

K_Hushii 🍁 2 years, 2 months ago

3median =mode + 2mean

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Omya Aryan 2 years, 2 months ago

3 Median = Mode + 2 Mean

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ANSWER

38. John and Jivanti are playing with the marbles in the playground. They together have 45 marbles and John has 15 marbles more than Jivanti. Then: (i) Find the number of marbles Jivanti had. (ii) Find the number of marbles John had. (iii) If 45 is replaced by 55 in the above case discussed in the question, then find the number of marbles Jivanti have.

Posted by Ankit Dangi 2 years, 2 months ago

CBSE > Class 10 > Mathematics

2 answers

A B 2 years, 2 months ago

yes..

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Omya Aryan 2 years, 2 months ago

(i) Jivanti had 15 marbles. (ii) Jhon had 30 marbles. (iii) If 45 is replaced by 55 in the above case, then Jivanti will have 20 marbles.

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ANSWER

the sum of sixth and ninth terms of the ap is 136 and 12th term and 15th term of the ap is 136 and 12th term and 15th term are 256 .find the AP

Posted by Nayana M S 2 years, 2 months ago

CBSE > Class 10 > Mathematics

2 answers

Surviver 🪐 2 years, 2 months ago

Given , a6+a9 = 136 a12+a15 = 136 a12+a15 = 256 Solu- Dys

1Thank You

Dushyant Shukla 1 year, 2 months ago

Chapter 3ka question 5

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ANSWER

Prove 5^ is irrational

Posted by Tanvi Tripathi 2 years, 2 months ago

CBSE > Class 10 > Mathematics

2 answers

Vidyut Kumaran 2 years, 2 months ago

We have to prove that √5 is an irrational number It can be proved using the contradiction method Assuming √5 as a rational number, i.e., can be written in the form a/b where a and b are integers with no common factors other than 1 and b is not equal to zero. √5/1 = a/b √5b = a By squaring on both sides 5b2 = a2 b2 = a2/5 .... (1) It means that 5 divides a2. It means that it also divides a a/5 = c a = 5c By squaring on both sides a2 = 25c2 Substituting the value of a2 in equation (1) 5b2 = 25c2 b2 = 5c2 Prove that √5 is irrational. b2/5 = c2 As b2 is divisible by 5, b is also divisible by 5 a and b have a common factor as 5 It contradicts the fact that a and b are coprime This has arisen due to the incorrect assumption as √5 is a rational number. Therefore, √5 is irrational. Prove that √5 is irrational. It is proved that √5 is irrational.

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Bhavnoorpreet Kaur 2 years, 2 months ago

Let us assume that 5^ is an rational number. So we have to find co-prime in the form of p/q where q is not equals to zero. Such that 2^ = p/q So b 2^=a 2b^2 =a^ According according to 1.8 divisible by 2 squarring on both sides =2^b^2 =a^2. Substituting the values we get 2c=a Substituting for a we get 2b^2=4c^2 B^2=2c^2 So this means that 2 / b^2 square and also divide by b therefore A and B have at least common factor but this contradict ic the no common factors rather than one this contradiction has been that due to our wrong assumption. So we concluded that it is irrational

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