Question

Which statement is true about the product square root of 2 (3 square 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.

Answer 1

equal to 12 is the answer

Answer 2

The correct option is A) It is rational and equal to 12.

Explanation:

Consider the provided information.

The provided expression is:

`√(2) (3√(2)+√(18))`

Further simplify the above expression.

`√(2) (3√(2)+√(2*\ 3 *3))`

`√(2) (3√(2)+3√(2))`

Now, use the distributive property:
`a(b+c)=ab+ac`

`3√(2)* {√(2)} +3√(2)*{√(2)}`

`3*{2}+3*{2}`

`6+6`

`12`

As 12 is a rational number. Thus, the correct option is A) It is rational and equal to 12.