Question

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

Answer 1

Step-by-step explanation:

Let √2+√5 be a rational number.

A rational number can be written in the form of p/q.

√2+√5=p/q

Squaring on both sides,

(√2+√5)²=(p/q)²

[√2²+√5²+2(√2)(√5)]=p²/q²

(2+5+2√10)=p²/q²

2√10+7=p²/q²

2√10=p²/q²-7

2√10=(p²-7q²)/q²

√10=(p²-7q²)/2q²

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

Then,√10 is also a rational number.

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

So,our supposition is false.

Therefore, √2+√5 is an irrational number.

Hence proved.

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