# 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.

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