Question

solve the following
1.(√5 - √2)^2​

Answer 1

$\sf\huge\bold{Answer:}$

Given :

$( \sqrt{5} - 2) {}^{2}$

Solution :

Using

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

we get,

$⇒( \sqrt{5} - 2) {}^{2} = { (\sqrt{5} )}^{2} + {2}^{2} - 2( \sqrt{5} )(2)$

Also,

$⇒ (\sqrt{x} ) {}^{2} = \sqrt{x} \times \sqrt{x} = \sqrt{x \times x} = \sqrt{ {x}^{2} } = x$

So,implementing this in our polynomial , we get

$= 5 + 4 - 4 \sqrt{5} \\ = 9 - 4 \sqrt{5}$

Hence,

$( \sqrt{5} - 2) {}^{2} = 9 - 4 \sqrt{5}$

Answer 2

Step-by-step explanation:

Solution:

Given that

(√5 - √2)^2

since, (a - b)^2 = a^2 - 2ab + b^2

Where, a = √5

and b = √2.

→ (√5)^2 - 2(√5)(√2) + (√2)^2

The square of √5 is 5.

The square of √2 is 2.

→ 5 - 2√(5 × 2) + 2

→ 5 - 2√(10) + 2

→ 7 - 2(√10) Ans.