Question

Prove that √3-√7 is irrational

Answer 1

Heyya !

To prove :-
√3-√7 is irrational

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Lets assume that √3-√7 is rational.

√3-√7 = r , where r is a rational number.

Squaring both the sides ,

[√3-√7 ]² = r²

3 - 2√21 +7 = r²

10 - 2√21 = r²

- 2√21 = r² - 10

√21 = r² - 10 / -2

Here ,

RHS is purely rational .
But , on the other hand , LHS is irrational [ √ 21 ]

This is a contradiction.

Hence , our assumption was wrong.

Thus , √3-√7 is irrational.

Hope this Helps You !!!!

Answer 2

Answer:

Step-by-step explanation:

To prove :-

√3-√7 is irrational

-----------------

Lets assume that √3-√7 is rational.

√3-√7 = r , where r is a rational number.

Squaring both the sides ,

[√3-√7 ]² = r²

3 - 2√21 +7 = r²

10 - 2√21 = r²

- 2√21 = r² - 10

√21 = r² - 10 / -2

Here ,

RHS is purely rational .

But , on the other hand , LHS is irrational [ √ 21 ]

This is a contradiction.

Hence , our assumption was wrong.

Thus , √3-√7 is irrational.

Hope this Helps You !!!!