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Show that there exists no rational …

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Show that there exists no rational number whose square is 5

Posted by Sona Budakoti 4 years, 10 months ago

CBSE > Class 10 > Mathematics

1 answers

Gaurav Seth 4 years, 10 months ago

Given,

Prove that there is no rational number whose square is

Let's assume that , where and and are co-prime.

Then we have,

So,

⇒

This implies that is even.

Then,

So,

⇒

Thus,

⇒

Then,

∴

which contradicts and being co-prime.

Therefore, is irrational.

1Thank You

ANSWER

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Posted by Kanika . 3 days, 1 hour ago

CBSE > Class 10 > Mathematics