Which statement is true about the product square root of 2(5 + square root of 8)?

Asked by maham237 @ 25/12/2020 in Mathematics viewed by 300 People

Which statement is true about the product square root of 2(5 + square root of 8)?
It is rational and equal to 7.

It is rational and equal to 9.

It is irrational and equal to 4 + square root of 10.

It is irrational and equal to 4 + 5square root of 2.

Answered by maham237 @ 25/12/2020

For this case we have the following product:

$\sqrt{2}(5+\sqrt{8})$

Applying the distributive property we have:

$5\sqrt{2}+\sqrt{2}\sqrt{8}$

Then, rewriting the expression we have:

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

$4+5\sqrt{2}$

We note that the answer is a irrational number, because the square root of two is not an exact number.

Answer:

$4+5\sqrt{2}$

It is irrational and equal to 4 + 5square root of 2.

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