Which statement is true about the product square root of 2(3square root of 2 + square root of 18)?
It is rational and equal to 12.
It is rational and equal to 18.
It is irrational and equal to 6 + 2 square root of 2.
It is irrational and equal to 3 + square root of 8.

Solution:

Given:

Product square root of 2(3square root of 2 + square root of 18)

By mathematically representing it as:

 √2 × (3√2 + √18)

The distributive property states that any expression with three numbers A, B, and C, given in form A (B + C) then it is resolved as:

A × (B + C) = AB + AC or A (B - C) = AB - AC.

This means operand A is distributed among the other two operands.

Using the distributive property,

= (3 × 2) + (√2 × √18)

So we get,

= 6 + √36

We know that √36 = 6

= 6 + 6

= 12

Therefore, the statement which is true is that it is rational and equal to 12.

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Which statement is true about the product square root of 2(3square root of 2 + square root of 18)?

Summary:

The statement which is true about the product square root of 2(3square root of 2 + square root of 18) is rational and equal to 12.