Question

simplify : (√5 + √2)² answer please​

Answer 1

(√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 :

Simplify the expression

We are aware of the identity that

(a + b)² = a² + 2ab + b²

Thus we get ,

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

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

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

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

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

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Answer 2

Answer:

The accurate answer is $7+2\sqrt{10}$.

Step-by-step explanation:

Concept:

In this we use formula $(a + b)^{2} = a^{2} + 2ab + b^{2}$ to solve it.

Given :

The expression $(\sqrt{5} +\sqrt{2} )^{2}$

To find :

We have to simplify the given expression.

Solution :

Write down the given expression

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

Simplify the expression using formula,

$(a + b)^{2} = a^{2} + 2ab + b^{2}$

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

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

$=7+2\sqrt{10}$

Thus we get ,$=7+2\sqrt{10}$