Math, asked by kapuruday28, 1 year ago

Prove that√3+2√5 is a irrational number.

Answers

Answered by nobelnagpal123
1

Let us assume that  √3+2√5 is rational number.

∴ √3+2√5=a/b where a and b are rational numbers.

squaring both sides,

(√3+2√5)²=a²/b²

⇒ 3+4√5+20=a²/b²

⇒23+4√5=a²/b²

⇒4√5=(a²/b²) -23

⇒√5=[(a²/b²)-23]/4

Now, it is clear that R.H.S. is rational but L.H.S. is irrational as√5 is irrational.

A rational number cannot be equal to an irrational number.

This contradicts our assumption.

Our assumption is wrong.

√3+2√5 is irrational.

HOPE IT HELPS YOU..

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