Question

when we Simplify (√5+√2)² we get the solution (√5)² + 2√5√2+ (√2)²= 5+2√10+2=7+2√10 how do we get 10?

Answer 1

The solution of $\bf ( { \sqrt{5} + \sqrt{2}) }^{2} = 7 + 2 \sqrt{10}$

Step-by-step explanation:

Given:

• $( { \sqrt{5} + \sqrt{2} ) }^{2}$

To find:

• Find the simplification of above written term.

Solution:

Concept /Formula to be used:

Identity to be used:

• $( {a + b)}^{2} = {a}^{2} + 2ab + {b}^{2}$
• $\sqrt{x} \times \sqrt{y} = \sqrt{x y}$

Step 1:

Compare the given terms with the identity.

On comparison of both, we get that

$a = \sqrt{5} \\ b = \sqrt{2}$

Apply the values in the identity.

So,

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

or

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

or

$( { \sqrt{5} + \sqrt{2} ) }^{2} = 7 + 2 \sqrt{5} \sqrt{2}$

Step 2:

Simplify the second term.

$( { \sqrt{5} + \sqrt{2} ) }^{2} = 7 + 2\red{ \sqrt{5} \sqrt{2} }$

or

$( { \sqrt{5} + \sqrt{2} ) }^{2} = 7 + 2 \sqrt{\red{5 \times 2}}$

or

$( { \sqrt{5} + \sqrt{2} ) }^{2} = 7 + 2 \sqrt{10}$

Thus,

The simplification of expression is

$\bf \: ( { \sqrt{5} + \sqrt{2} ) }^{2} = 7 + 2 \sqrt{10}$

By this way we get 10 under square root.

Learn more:

1) What is answer 3 root 2 whole square

https://brainly.in/question/17436083

2) On adding 2√3 and 3√2 we get:

a) 5√5

b) 5(√3+√2)

c) 2√3+ 3√2

d) none of the above

https://brainly.in/question/18360370

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