CBSE > Class 10 > Mathematics | CBSE Board | Homework Help

Let us assume that {tex}\sqrt2{/tex} is a rational number.
So it can be expressed in the form p/q where p, q are co-prime integers and q {tex}\ne{/tex} 0
{tex}\sqrt2{/tex} = p/q
Here p and q are coprime numbers and q {tex}\ne{/tex} 0
Solving
{tex}\sqrt2{/tex} = p/q
On squaring both the side we get,
{tex}\Rightarrow{/tex} 2 = (p/q)²
{tex}\Rightarrow{/tex} 2q² = p² .. (1)
p²/2 = q²
So 2 divides p and p is a multiple of 2.
{tex}\Rightarrow{/tex} p = 2m
{tex}\Rightarrow{/tex} p² = 4m² ..(2)
From equations (1) and (2), we get,
2q² = 4m²
{tex}\Rightarrow{/tex} q² = 2m²
{tex}\Rightarrow{/tex} q² is a multiple of 2
{tex}\Rightarrow{/tex} q is a multiple of 2
Hence, p, q have a common factor 2. This contradicts our assumption that they are co-primes. Therefore, p/q is not a rational number
{tex}\sqrt2{/tex} is an irrational number.

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Mayank Choudhary 4 years, 7 months ago

Let us assume that ✓2 is a rational number. So it can be expressed in the form p/q where p, q are co-prime integers and q 0 = p/q Here p and q are coprime numbers and q 0 Solving = p/q On squaring both the side we get, 2 = (p/q)2 2q2 = p2 .. (1) p2/2 = q2 So 2 divides p and p is a multiple of 2. p = 2m p2 = 4m2 ..(2) From equations (1) and (2), we get, 2q2 = 4m2 q2 = 2m2 q2 is a multiple of 2 q is a multiple of 2 Hence, p, q have a common factor 2. This contradicts our assumption that they are co-primes. Therefore, p/q is not a rational number Hence it is proved that ✓2 is irrational number

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ANSWER

factorise 25x^2 -36y^2

Posted by Priyanka Jha 4 years, 7 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 4 years, 7 months ago

25x² - 36y²
= (5x)² - (6y)²
= (5x + 6y) (5x - 6y)

8Thank You

ANSWER

If a(6 -1) and c(k 8) are three points such that ab=bc find the value of k.

Posted by Simran Kumari 4 years, 7 months ago

CBSE > Class 10 > Mathematics

5 answers

Kshitiz Mishra 4 years, 7 months ago

GivenA(6,−1),B(1,3) and C(k,8) Using distance formula AB 2 =BC 2 ⇒(6−1) 2 +(−1−3) 2 =(k−1) 2 +(8−3) 2 ⇒25+16=k 2 +1−2k+25 ⇒k 2 −2k−15=0 ⇒k 2 −5k+3k−15=0 ⇒k(k−5)+3(k−5)=0 ⇒(k−5)(k+3)=0 k−5=0⇒k=5 k+3=0⇒k=−3

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Anuradha Chaudhary 4 years, 7 months ago

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Anuradha Chaudhary 4 years, 7 months ago

You haven't given b(1,3 ) in your question

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Anuradha Chaudhary 4 years, 7 months ago

Wait i am answering

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Anuradha Chaudhary 4 years, 7 months ago

Didn't understand question

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ANSWER

In the given figure, DE || BC, AD = 2 cm, BD = 2.5 cm, AE = 3.2 cm and DE =4 cm. Find AC and BC.

Posted by Sayyad ... 4 years, 7 months ago

CBSE > Class 10 > Mathematics

3 answers

Adithya Dev A 4 years, 7 months ago

AD/BD = AE/EC ....... AD/(AD+BD) = DE / BC. Use these formulas. (ΔADE ~ ΔABC)

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Anuradha Chaudhary 4 years, 7 months ago

AC =7.2

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Pranav Jp 4 years, 7 months ago

Where is the figure?

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if 5 is rational and -root3 is irrational then what is 5+foot 3

Posted by Aditi Sharma 4 years, 7 months ago

CBSE > Class 10 > Mathematics

2 answers

Anuradha Chaudhary 4 years, 7 months ago

Irrational

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Hk Honey 4 years, 7 months ago

Hey

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ANSWER

√5 is a irrational

Posted by Abhinav Jha 4 years, 7 months ago

CBSE > Class 10 > Mathematics

5 answers

Anuradha Chaudhary 4 years, 7 months ago

We prove by contradiction method. Let assume that √5 is rational. √5=p/q ---eq......1 P and q are co prime integer with common factor 1. Squaring both side equation 1 5=p²/q² :. q²=p²/5 eq...2 It means p² have factor 5 so p would also have sector 5. p=5x squaring both side p²=25x² Puting this value of p² in equation 2 q²=25x²/5 q²=5x² q²/5=x² This means q² have factor 5. But our assumption says p and q have common factor 1. So our assumption was wrong √5 is irrational number.

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Mamta ... 4 years, 7 months ago

yes √ 5 is an irrational no.

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Ayan Patel 4 years, 7 months ago

Let 5 be a rational number. then it must be in form of qp where, q=0 ( p and q are co-prime) 5=qp 5×q=p Suaring on both sides, 5q2=p2 --------------(1) p2 is divisible by 5. So, p is divisible by 5. p=5c Suaring on both sides, p2=25c2 --------------(2) Put p2 in eqn.(1) 5q2=25(c)2 q2=5c2 So, q is divisible by 5. . Thus p and q have a common factor of 5. So, there is a contradiction as per our assumption. We have assumed p and q are co-prime but here they a common factor of 5. The above statement contradicts our assumption. Therefore, 5 is an irrational number.

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Ayan Patel 4 years, 7 months ago

√5 =p/q

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Ayan Patel 4 years, 7 months ago

Let us assume that√5 is rational

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ANSWER

Find zeros of tsq-15

Posted by Srishti Meemansa 4 years, 7 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 4 years, 7 months ago

First, write the equation,
t² - 15 = 0
Now, we shift the (-15) to RHS,
t² = 15
So, t = - {tex}\sqrt {15}{/tex} = -3.87 or + {tex}\sqrt {15}{/tex} = + 3.87

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ANSWER

225 का 35% कितना होगा

Posted by Aman Gupta 4 years, 7 months ago

CBSE > Class 10 > Mathematics

3 answers

Mayank Choudhary 4 years, 7 months ago

= 78.75

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Tanu Srivastava 4 years, 7 months ago

78.75

3Thank You

Mamta ... 4 years, 7 months ago

225÷100*35 = 78.75

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ANSWER

Aaplog maths ke liye ncert ke alawa koi side book use krte ho kya??

Posted by Tanu Srivastava 4 years, 7 months ago

CBSE > Class 10 > Mathematics

5 answers

Mamta ... 4 years, 7 months ago

yes i use exemplar

2Thank You

Oav Papadahandi 4 years, 7 months ago

Right Aman

1Thank You

Aman Gupta 4 years, 7 months ago

Are phela ncert fir rd

3Thank You

Tanu Srivastava 4 years, 7 months ago

What pyq

3Thank You

Simran Rathore 4 years, 7 months ago

No After solving ncert i prefer to solve pyq

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ANSWER

Cos thetha=0.6, show that (5sin thetha-3tan thetha) =0.

Posted by Kashish Garg 4 years, 7 months ago

CBSE > Class 10 > Mathematics

1 answers

Simran Rathore 4 years, 7 months ago

Given=cosA=0.6 CosA=B/H 0.6=B/H 6/10=B/H Base=6 Hypo.=10then by using pythagoras theorem Perpendicular =8 Prove: 5sinA-3tanA=0 5×P/H-3×P/B=0 5×8/10-3×8/6=0 4-4=0 0=0 Hence proved

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Sec thetha=5/4, verify that tan thetha/(1+tansquare thetha) =sin thetha/sec thetha

Posted by Kashish Garg 4 years, 7 months ago

CBSE > Class 10 > Mathematics