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Prove that the Following is Irrational 7 √ 5 - Mathematics

Sum

Prove that the following is irrational

` 7sqrt5`

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Solution

Let a = `7sqrt5` be a rational number.

⇒ `a/7 = sqrt5.`

Now, `a/7` is a rational number since product of two rational number is a rational number.

The above will imply that `sqrt5` is a rational number. But `sqrt5 ` is an irrational number.

This contradicts our assumption. Therefore we can conclude that `7sqrt5` is an irrational number and hence the result.

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APPEARS IN

NCERT Class 10 Maths
Chapter 1 Real Numbers
Exercise 1.3 | Q 3.2 | Page 14
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