Question

the value of (√5+√2)²

Answer 1

(a+b)²=a²+b²+2ab.

Therefore

(√5+√2)²= (√5)²+(√2)²+2(√5)(√2)

=5+2+2(√10)

=7+2√10.

Answer 2

(√5 + √2)² = 7 + 2√10

Given :

The expression (√5 + √2)²

To find :

To simplify the expression

Formula :

(a + b)² = a² + 2ab + b²

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

(√5 + √2)²

Step 2 of 2 :

Find the value of the expression

We use the formula (a + b)² = a² + 2ab + b²

Thus we get

$\displaystyle \sf{ {( \sqrt{5} + \sqrt{2} )}^{2} }$

$\displaystyle \sf{ = {( \sqrt{5} )}^{2} + 2 \times \sqrt{5} \times \sqrt{2} + {( \sqrt{2} )}^{2} }$

$\displaystyle \sf{ = 5 + 2 \sqrt{10} + 2 }$

$\displaystyle \sf{ = 7 + 2 \sqrt{10} }$

Hence (√5 + √2)² = 7 + 2√10

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