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.

Solution:

It is given that product square root of 2(5 + square root of 8)

We can write it as

√2(5 + √8)

Using the multiplicative distributive property 

√2(5 + √8) = 5√2 + √2 × √8 = 5√2 + √16

Here √16 = 4

√2(5 + √8) = 5√2 + 4

Therefore, the statement which is true is that it is irrational and equal to 4 + 5square root of 2.

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

Summary:

The statement which is true about the product square root of 2(5 + square root of 8) is that it is irrational and equal to 4 + 5square root of 2.