Question

evaluate(√5+2√2)²-(√5-2√2)²

Answer 1

ANSWER

25.2982212813

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Answer 2

Answer:

The value of $(\sqrt{5} + 2\sqrt{2} )^{2} - (\sqrt{5} - 2\sqrt{2} )^{2}$ is $= 8\sqrt{10}$

Step-by-step explanation:

Given : $(\sqrt{5} + 2\sqrt{2} )^{2} - (\sqrt{5} - 2\sqrt{2} )^{2}$

To find: Simplify and find the values of the given equation.

Formula used:$a^{2} - b^{2} = (a+b)(a-b)$

Solution:

The given equation is

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

Let us take

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

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

Evaluation can be defined as finding  the value of the expression when the variable is replaced by a given number.

We know that ,

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

Substitute the values in the formula

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

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

Simply the given term

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

Same number with the opposite sign has been neglected.

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

$=( 2\sqrt{5} ).(4\sqrt{2} )$

$= 8\sqrt{10}$

Final answer

The value of the given expression $(\sqrt{5} + 2\sqrt{2} )^{2} - (\sqrt{5} - 2\sqrt{2} )^{2}$ is $8\sqrt{10}$

 #SPJ2