No products in the cart.

Prove that √5 is irrational number.

CBSE, JEE, NEET, CUET

CBSE, JEE, NEET, CUET

Question Bank, Mock Tests, Exam Papers

NCERT Solutions, Sample Papers, Notes, Videos

Prove that √5 is irrational number.

Posted by Bhuvaneshwari Shivapur 1 year, 6 months ago

CBSE > Class 10 > Mathematics

3 answers

Kaushik Krishna 1 year, 6 months ago

Let √5 a rational number Where √5=a/b and a and b are co primes and b not equal to 0 Square them 5=a square / b square Cross multiply 5b square is equal to a square B is a factor of a B is also a factor of a square Now take A is equal to 5 c Square them A square is equal to 25 c square We know that a square is equal to 5 b square So now 5 b square is equal to 25 c square Simplify them We get b square is equal to 5 c square Now 5 is a factor of b square and b It contradict to our assumption that a and b are co primes Hence our assumption is wrong Therefore √5 is an irrational number Hence proved

Sureksha Sp 1 year, 6 months ago

Let √5 a rational number Where √5=a/b and a and b are co primes and b not equal to 0 Square them 5=a square / b square Cross multiply 5b square is equal to a square B is a factor of a B is also a factor of a square Now take A is equal to 5 c Square them A square is equal to 25 c square We know that a square is equal to 5 b square So now 5 b square is equal to 25 c square Simplify them We get b square is equal to 5 c square Now 5 is a factor of b square and b It contradict to our assumption that a and b are co primes Hence our assumption is wrong Therefore √5 is an irrational number Hence proved

Joshi Priya Dharmeshkumar 1 year, 6 months ago

Let √5 =a/b (where a/b is an rational number where a/b are co-primes) Squaring both the sides 5 = a2/b2 5b2 = a2 ---1 Thus 5 divides a2 , 5 divides a Now take any other integer as c such that a=5c squaring both the sides a2=25c2 --- 2 put a value from eq-1 into eq-2 5 b2 =25 c 2 b2=5c2 5 divides b2 and 5 divide b We let a&b are co-primes but here we are getting 5 as a factor of both a &b. So our prediction that a&b are co-primes is wrong Thus ✓5 is an Irrational number.

ANSWER

http://mycbseguide.com/examin8/

Related Questions

Find the sum of the odd no. Between 0 and 50

Posted by Kanika . 2 months ago

CBSE > Class 10 > Mathematics

1 answers

X-y=5

Posted by Kishan Thakur 1 month, 3 weeks ago

CBSE > Class 10 > Mathematics

1 answers

Find the nature of quadratic equation x^2 +x -5 =0

Posted by Parinith Gowda Ms 3 months, 4 weeks ago

CBSE > Class 10 > Mathematics

0 answers

sin60° cos 30°+ cos60° sin 30°

Posted by Vanshika Bhatnagar 3 months, 4 weeks ago

CBSE > Class 10 > Mathematics

2 answers

If 1/2 is a root of equation x^2+kx- 5/4 =0 , then what is the value of k

Posted by Parinith Gowda Ms 3 months, 4 weeks ago

CBSE > Class 10 > Mathematics

1 answers

Water

Posted by S Prajwal 2 weeks, 1 day ago

CBSE > Class 10 > Mathematics

0 answers

Is it possible to design a rectangular mango Grove whose length is twice it's breadth, and the area is 800m²? If so, find it's length and breadth

Posted by Akshata Choukse 3 months, 4 weeks ago

CBSE > Class 10 > Mathematics

0 answers

Venu Gopal has twice

Posted by Lakshay Kumar 1 week ago

CBSE > Class 10 > Mathematics

0 answers

(A + B )²

Posted by Abhishek Gupta 3 months, 4 weeks ago

CBSE > Class 10 > Mathematics

1 answers

Find cosec 30 degree and cause 60 degree geometrical

Posted by Hari Anand 2 weeks, 1 day ago

CBSE > Class 10 > Mathematics

0 answers

myCBSEguide App

myCBSEguide

Trusted by 1 Crore+ Students

Test Generator

Test Generator

Create papers online. It's FREE.

CUET Mock Tests

CUET Mock Tests

75,000+ questions to practice only on myCBSEguide app

Google Play

Download myCBSEguide App