Math, asked by Unique1809, 7 months ago

Show 5+root 7 is irrational

Answers

Answered by snehitha2

Let 5 +√7 be a rational number.

A rational number can be written in the form of p/q where p,q are integers.

5 +√7 = p/q

5 = p/q-√7

Squaring on both sides,

(5)² = (p/q-√7)²

25 = p²/q² + √7² - 2(p/q)(√7)

√7×2p/q = p²/q²+7-25

√7 = p²/q² - 18

√7 = (p²-18q²)/q² × q/2p

√7 = (p²-18q²)/2pq

p,q are integers then (p²-18q²)/2pq is a rational number.

Then, √7 is also a rational number.

But this contradicts the fact that √7 is an irrational number.

So,our supposition is false.

Therefore, 5+√7 is an irrational number.

Also refer :

https://brainly.in/question/1380388

https://brainly.in/question/2179266

HOPE IT HELPS..!

Answered by anjalivrm2000

:we know that √7 is an irrational number.

:we know that √7 is an irrational number.The sum of rational number and an irrational number is always irrational number

5 is a rational number

√7 is an irrationa number

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