Question

Prove that 5 – √3 is an irrational number.plz ans fast​

Answer 1

SOLUTION :

Let us assume that 5 - √3 is rational.

5 - √3 = a/b (a and b are co-primes)

5 - a/b = √3

√3 = 5 - a/b

After LCM,

√3 = (5b - a)/b

a, b and 5 are integers we get 5 - a/b so √3 is rational.

but, we know that √3 is irrational.

Our assumption is wrong as √3 = (5b - a)/b is irrational.

Hence, we conclude that, 5 - √3 is irrational.

Answer 2

Answer :-

Step by step explanation

$\rule{200}{1}$

Let 5-√3 be a rational number

So,

5-√3 = a/b

(Where b is ≠ 0 , a and b are co-prime numbers)

5-√3 = a/b

Cross multiply both side

-√3 = a/b-5

-√3 = 5a/b

____________[ Take L. C. M ]

√3 = -5a/b

Hence, our supposition was wrong because √3 is irrational number and can't be equal to -5a/b , which is rational.

So, 5-√3 is irrational number.

$\rule{200}{1}$