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Root 3 is irrational no. Prove

Posted by Sumit Kumar 6 years, 11 months ago

CBSE > Class 10 > Mathematics

2 answers

Yogita Ingle 6 years, 11 months ago

Let us assume that √3 is a rational number
That is, we can find integers a and b (≠ 0) such that √3 = (a/b)
Suppose a and b have a common factor other than 1, then we can divide by the common factor, and assume that a and b are coprime.
√3b = a
⇒ 3b²=a2 (Squaring on both sides) → (1)
Therefore, a²is divisible by 3
Hence a is also divisible by 3.
So, we can write a = 3c for some integer c.
Equation (1) becomes,
3b² =(3c)²
⇒ 3b² = 9c²
∴ b² = 3c²
This means that b² is divisible by 3, and so b is also divisible by 3.
Therefore, a and b have at least 3 as a common factor.
But this contradicts the fact that a and b are coprime.
This contradiction has arisen because of our incorrect assumption that √3 is rational.
So, we conclude that √3 is irrational.

Afzal Siddique 6 years, 11 months ago

Root3=irrational no. Hence proved.

ANSWER

Find all zeroes of 2x^4-3x^3-3x^2+6x-2 if two of its zeroes are 1 and 1/2

Posted by Anku Don 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Priyanka S 6 years, 11 months ago

(x-1)(x-1/2) solve this and divide the polynomial by the equation solved u will get the other zeroes

ANSWER

Cot19 cot 52 cot 38 cot 78 cot 60 evaluate this

Posted by ??Ratnakar ?? Pisal 6 years, 11 months ago

CBSE > Class 10 > Mathematics

0 answers

ANSWER

Respected sir i want to know that from which chapter how many marks are coming in 10thboard examination. And also tell me about this time board pattern is it will be easy as last year or some changess???

Posted by Aditya Gupta 6 years, 11 months ago

CBSE > Class 10 > Mathematics

2 answers

Anwaya Kumar Nayak 6 years, 11 months ago

Search in you tube

Afzal Siddique 6 years, 11 months ago

Please login cbse.nic.in

ANSWER

A boat travells 24km with upstream and downstream the speed of boat is 18km/h it takes 1hour more in upstream compare to downstream.find the speed of stream (give answer with step)

Posted by Sudhanshu Singh 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Roshan Meshram 6 years, 11 months ago

Let the speed of boat. X km/h The speed of boat in upstream= (24-x)km/h The speed of boat in downstream =. (24+x)km/h 24÷(24-x). 24(24+x). Multiples both sides X squares+48x-324=0. X commen (X+56) (x-6) X#0 x=0 Hence the speed of the boat is 6km/h

ANSWER

The differences between the outside and inside surface areas of cylindrical metallic pipe of 14cm long is 88cm'2 .

Posted by Sunil Kumar 6 years, 11 months ago

CBSE > Class 10 > Mathematics

0 answers

ANSWER

Show that the sum of all odd integers between1to 1000 divisible by 3is 83667

Posted by Kiran Yadav 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Navneet Verma 6 years, 11 months ago

A.P : 3,9,15,------------999. Here a= 3, d=6, An = 999. An= a+ (n-1)d 999=3 + ( n-1)6 999=3+ 6n - 6 999 = 6n- 3 999+3=6n 1002=6n 1002/6=n 167=n. Sn = n/2 [2a+(n-1) d ] S167 = 167/2 [2×3+(167-1)×6] = 167/2 [6+166×6] = 167/2 [1002] = 167/2× 1002 =167×501 = 83667. Hence proved

ANSWER

How to capare the area

Posted by Sameer Khan 6 years, 11 months ago

CBSE > Class 10 > Mathematics

0 answers

ANSWER

AP is s tangent to the circle with centre O. If BC =3cm AC=4 cm and ∆ACB similar to ∆APO then find OA and OP/AP

Posted by Kiran Yadav 6 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 4 months ago

BC = 3 cm, AC = 4 cm and {tex}\triangle ACB\sim \triangle PAO{/tex}
In {tex}\triangle ACB{/tex},

{tex}\angle BCA=90^o{/tex} [angle in a semi-circle]

{tex}\therefore {/tex} AB² = AC² + BC² [By Pythagoras theorem]

{tex}\Rightarrow{/tex} AB² = 4² + 3²
{tex}\Rightarrow{/tex} AB² = 16 + 9 cm
{tex}\Rightarrow{/tex} AB² = 25 cm
{tex}\Rightarrow{/tex} AB = 5 cm
{tex}\Rightarrow OA =\frac{AB}{2} =\frac{5}{2}cm{/tex}

Also given, {tex}\triangle ACB\sim \triangle PAO{/tex}

{tex}\therefore \frac{AB}{AC}=\frac{OP}{AP}{/tex}
{tex}\Rightarrow \frac{OP}{AP}=\frac{5}{4}{/tex}

ANSWER

What are dacimal

Posted by Honey Ahlawat 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Rohit Yadav 6 years, 11 months ago

A decimal is a fraction that is written in the form of a dot followed by one or more numbers which represent tenths, hundredths, and so on

ANSWER

find zeroes of t^2- 10

Posted by Shriya ?? 6 years, 11 months ago

CBSE > Class 10 > Mathematics

7 answers

Shriya ?? 6 years, 11 months ago

do u understand (fam is nothing i was just confusing u)

Shriya ?? 6 years, 11 months ago

i hope good give u power to understand the meaning of this and all the best for your exam

Neeraj 17_ 6 years, 11 months ago

1 thing i ask from u

Shriya ?? 6 years, 11 months ago

what can i ask no ques . but if u want to ask then u can ask

Shriya ?? 6 years, 11 months ago

okay

Neeraj 17_ 6 years, 11 months ago

?

Avinash Saigal 6 years, 11 months ago

T^2 -10=0 T^2 = 10 T = √10 T = +_ 10 That is T has two value either 10 or -10. Thank you??

ANSWER

Two dice are thrown at the same time. Determine the probability that the difference of numbers on two dice is 0and 2

Posted by Puja Kaushal 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Avinash Saigal 6 years, 11 months ago

Answer is:- 7/18

ANSWER

euclid division lemma states that for any 2 +ve integer A and B there exists unique integer Q and R such that a= bq+ r then what is value of r?

Posted by Shriya ?? 6 years, 11 months ago

CBSE > Class 10 > Mathematics

6 answers

Shriya ?? 6 years, 11 months ago

no

Shriya ?? 6 years, 11 months ago

okay

Shriya ?? 6 years, 11 months ago

maths ka paper aacha nahi hua kya???

Shriya ?? 6 years, 11 months ago

law

Neeraj 17_ 6 years, 11 months ago

11 which subj

Neeraj 17_ 6 years, 11 months ago

What

ANSWER

Find value of which one root of quadratic equations kxsquare -14x+18=0 is 2

Posted by Priya Sharma 6 years, 11 months ago

CBSE > Class 10 > Mathematics

2 answers

@Jay Bunkar 6 years, 11 months ago

K=5

Priya Sharma 6 years, 11 months ago

Value of k

ANSWER

SinA-cosA+1/sinA+cosA-1=tanA-1+secA/tanA+1-secA

Posted by Santosh Singh 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Gaurav Seth 6 years, 11 months ago

Q.SinA-cosA+1/sinA+cosA-1=tanA-1+secA/tanA+1-secA

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Answer:

ANSWER

Empheric relationship between to find central tendency

Posted by Abhay Singh 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Allan Krish 6 years, 11 months ago

Mode=3median-2mean

ANSWER

Formulas of surface area volume

Posted by Anushka Dpsnk 6 years, 11 months ago

CBSE > Class 10 > Mathematics

0 answers

ANSWER

Whats the formula of vol. Of frustum???

Posted by Aarohi Singh 6 years, 11 months ago

CBSE > Class 10 > Mathematics

4 answers

Sonu 6 years, 11 months ago

1/3 PIE ×HEIGHT (R ^2+ r^2+Rr)

@ Aashu 6 years, 11 months ago

1/3pie h ( r2 + R 2 + r.R )

Aarohi Singh 6 years, 11 months ago

Ťhanks?

Rahul Raj 6 years, 11 months ago

1/3πh(R^2 + r^2 +Rr)

ANSWER

In an ap the sum of first 6terms to the sum of first 10terms are in the ratio of 3 :7 if 16th term is 3(a5-4) find the progression

Posted by Shivam Shivam 6 years, 11 months ago

CBSE > Class 10 > Mathematics

0 answers

ANSWER

Question no.4 Of exercise 8.2

Posted by Niraj Chaurasiya 6 years, 11 months ago

CBSE > Class 10 > Mathematics

0 answers

ANSWER

If the quadratic equation of px square -2root 5 px +15 =0 has two equal roots then find p

Posted by Pradeepa Govind 6 years, 11 months ago

CBSE > Class 10 > Mathematics

2 answers

Rahul Raj 6 years, 11 months ago

Now solve your self

Rahul Raj 6 years, 11 months ago

For equal roots , b^2 -4ac =0

ANSWER

a3 +b3

Posted by Nikhil Gangwani 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Anjani Kumar Singh 6 years, 11 months ago

a+b^3-3ab(a+b)

ANSWER

What is the common difference of an A.P. in which a 21  a 7 = 84 ?

Posted by Abdullah Shams 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Raj Kaushal 6 years, 11 months ago

9

ANSWER

4tan=3, evaluate (4sin-cos+1/4sin+cos-1)

Posted by Aadesh Singh 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Priyanka S 6 years, 11 months ago

13/21

ANSWER

Surface area and volume rd sharma

Posted by R Means Räkésh 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Janhvi Bora 6 years, 11 months ago

Surface area and volume rd sharma mein kya nahi aara hai???

ANSWER

In figure,is shown a right circular cone of 30cm. A small cone is cut off from the top by a plane parallel to the base. If the volume of the small cone is 1/27 of the volume of given cone , find at what height above the base is the section made

Posted by Anchal Negi 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

D.J Alok 6 years, 11 months ago

Where is the figure???????

ANSWER

Sum of the areas of two squares is 468msquare . If the difference of their perimeter is 24m , find the sides of the 2 squares??

Posted by Anshika Pal???? 6 years, 11 months ago

CBSE > Class 10 > Mathematics

3 answers

Neha Sirur 6 years, 11 months ago

Perimeter =4x Diffrence is 24 4x=24+4x X=x+6 which is the length of each side Sum of areas is 468m2 X^2+ (6+x)^2= 468 X^2+6x-216=0 Solve it ans is 18 and 12

Puja Sahoo? 6 years, 11 months ago

18m, and 12m.its ncert question yu can check in this app.

Neha Sirur 6 years, 11 months ago

It is ncert text bk question exercise 4.3

ANSWER

Two taps in which capacity of First tap largest capacity is 4.5 times the second tap. Which can empty the tank in 9 hours .If they work together latest 7.5 hours how much time that tap take with smaller capacity.

Posted by Janhvi Mahajan 6 years, 11 months ago

CBSE > Class 10 > Mathematics

0 answers

ANSWER

5^(2x) -5^(x+2) +125=5^(x)

Posted by Varun Punia 6 years, 11 months ago

CBSE > Class 10 > Mathematics

3 answers

Neha Sirur 6 years, 11 months ago

Is it 5 to the power 2x???

Varun Punia 6 years, 11 months ago

It may be quadratic equation

Varun Punia 6 years, 11 months ago

Plz answe

ANSWER

Show that 5-2√3irrantion number

Posted by Digraj Chouhan 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Avinash Saigal 6 years, 11 months ago

assume that 5-2 root 3 is rational 5-2 root 3 = a/b , where a and b are integers . -2 root 3 = a/b - 5 2 root 3 = 5 - ab 2 root 3 = 5b/b - a/b root 3 = 5b - a / 2b we know that a, b , 2 and 5 are integers and they are also rational therefore root 3 will be rational but we know that root 3 is irrational there is a contradiction so, 5 - 2 root 3 is an irrational number. Thank you??

ANSWER

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