Question

(√3-√7)² simplify this ​

Answer 1

Given:

The expression -

• (√3 - √7)²

What To Find:

We have to -

• Simplify the expression.

Identity Used:

• (a - b)² = a² + b² - 2ab

Solution:

Using the identity,

⇒ (a - b)² = a² + b² - 2ab

Where,

• a = √3
• b = √7

So it will be,

⇒ (√3)² + (√7)² - 2(√3 × √7)

Find the square of √3,

⇒ 3 + (√7)² - 2(√3 × √7)

Find the square of √7,

⇒ 3 + 7 - 2(√3 × √7)

Find √3 × √7,

⇒ 3 + 7 - 2 × √21

Find 2 × √21,

⇒ 3 + 7 - 2√21

Find 3 + 7,

⇒ 10 - 2√21

Final Answer:

∴ Thus, the value of the expression is 10 - 2√21.

Answer 2

It can be done using following identity:

$( \sqrt{x} - \sqrt{y} ) ^{2} = x + y - 2 \sqrt{xy}$

It is solved as follows.

$( \sqrt{3} - \sqrt{7} )^{2} \\= 3 + 7 - 2 \sqrt{3 \times 7} \\ = 10 + 2 \sqrt{21}$