Question

Prove that 5-2√7 is irrational

Answer 1

Hi friend
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Your answer
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To prove : - 5 - 2√7 is irrational.

Now,
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√7 = 2.6457513110........

It is a non terminating and non repeating decimal. so, √7 is irrational.

Now,
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We know that ,
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(Rational number ) × (Irrational number ) = Irrational number.

so,
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2 × √7 = 2√7 (irrational)

Again,
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(Rational number) - (Irrational number) = Irrational number

So,
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5 (Rational) - 2√7 (Irrational) = 5 - 2√7 (Irrational)

Therefore,
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5 - 2√7 is an irrational number.

HOPE IT HELPS