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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.

User Luis Perez
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2 Answers

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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.
User Geg
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For this case we have the following product:


√(2)(5+√(8))

Applying the distributive property we have:


5√(2)+√(2)√(8)

Then, rewriting the expression we have:


2√(2)√(2)+5√(2)


4+5√(2)

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

Answer:


4+5√(2)

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

User Enriquein
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