Question

prove that √ 2 + √ 5 is an irrational number​

Answer 1

Hope you will better understand .

See my answer.

Answer 2

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Let's assume √2+√5 to be a rational number.

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

√2+√5 = $\frac{p}{q}$

Squaring on both sides,

(√2+√5)² = ($\frac{p}{q}$)²

√2²+√5²+2(√5)(√2) = p²/q²

2+5+2√10 = p²/q²

7+2√10 = p²/q²

2√10 = p²/q² - 7

√10 = (p²-7q²)/2q

p,q are integers then (p²-7q²)/2q is a rational number.

√10 is a rational number.

But this contradicts the fact that √10 is an irrational number.

.°. Our assumption is wrong

√2+√5 is an irrational number.I

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