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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.

Respuesta :

meerkat18
We are given with two factors: square root of 2 and 5 + square root of 8. We use a scientific calculator that displays irrational answers. The product of the two factors is 4 + 5 square root of 2. The answer is irrational since the square root sign in the answer is present.
carlosego

For this case we have the following product:

[tex] \sqrt{2}(5+\sqrt{8}) [/tex]

Applying the distributive property we have:

[tex] 5\sqrt{2}+\sqrt{2}\sqrt{8} [/tex]

Then, rewriting the expression we have:

[tex] 2\sqrt{2}\sqrt{2}+5\sqrt{2} [/tex]

[tex] 4+5\sqrt{2} [/tex]

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

Answer:

[tex] 4+5\sqrt{2} [/tex]

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

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