Question

Use the properties of radicals to simplify the expression. Explain.

Answer 1

Because both 2 and 72 under the radical are positive numbers, we can apply this rule:

`√(2)\cdot√(72) = √(2\cdot72)`

Now that new version,
`√(2\cdot 72)` is the same thing as
`√(144)`, because
`2\cdot72=144`.

And
`√(144)=12`.

12 is your answer.

The rule we used is
`√(a)\cdot√(b) = √(a\cdot b)`, but it only works if both
`√(a)` and
`√(b)` are real numbers (AKA if a and b are both non-negative).