Question

How do you multiply `\sqrt { 130} \cdot \sqrt { 26}`?

Answer 1

See below.

Explanation:

Whenever you multiply two square roots, you can simply do this:

`sqrt(130) * sqrt(26)`

`sqrt(130*26)`

This is a very useful tool, as you will find later on in mathematics. Anyway, let's simplify this further:

`sqrt(130*26)`

`sqrt(3380)`

This is not yet in simplest form, so we will have to factor the term under the `sqrt` in order to reach the final answer in simplest form. You may want to do the prime factorization of `3380` on paper first:

`sqrt(3380)`

`sqrt(2^2 * 5 * 13^2`

Now, we need to use the square root to remove the `2^2` and `13^2` from inside the radical:

`sqrt(2^2 * 5 * 13^2`

`(2*13)sqrt(5)`

`26sqrt(5)`

This is your final answer (`26sqrt(5)`), and it cannot be simplified any further.

I hope that helps!