Question

show that 5+√7

is an irrational number​

Answer 1

Answer:

Let us assume that

5 + √7 is a rational

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number. 5+√7 = where p and q are two integers and q # 0

Since, p,q and 5 are integers, so p - 5q is a

p - 5q = rational number. But this contradicts the fact that √7 is an irrational number. This contradiction has arisen due to our assumption that 5+√7 is a rational number.

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→ √7 is also a rational number.

Hence, 5 + √7 is an irrational number

Answer 2

Answer:

$\huge\fbox\green{Answer}$

Step-by-step explanation:

Let us assume that 5+√7

Let us assume that 5+√7 is a rational number.

Then 5+√7 =

$\frac{p}{q}$

, where p and q are two integers and q(R not equal}0

$\sqrt{7} = \frac{p}{q} - 5 = \sqrt{7} = \frac{p - 5q}{q}$

Since, p, q and 5 are integers, so

$\frac{p - 5q}{q}$

is a rational number.

is a rational number.Therefore

is a rational number.Therefore

√7 is also a rational number.

is also a rational number.But this contradicts the fact that √7

is an irrational number.

is an irrational number.This contradiction has arisen due to our assumption that 5√7

is a rational number.

is a rational number.Hence,5 √7

is an irrational number.