Simplify 6√5 × 2√15

Step by step

The question

Question: work out 6√5 × 2√15.

1 Multiply

Rule: two roots times each other make one root of the two numbers times each other.

Times can go in any order.

So we put the numbers outside together, and the roots together.

6 times 2 is 12.

So it is 12 times the root of 5 times 15.

Careful!

This works for times, not for plus.

√9 + √16 is 3 + 4 = 7, but √25 is 5.

5 times 15 is 75.

2 Simplify the root

Now we make √75 simpler, like in the lesson on square roots.

36 does not go into 75.

The biggest square that goes into 75 is 25: 75 divided by 25 is 3.

So √75 is √25 times √3.

√25 is 5, because 5 times 5 is 25.

12 times 5 is 60.

So we get 60√3.

So 6√5 × 2√15 = 60√3.

3 Check

Let's check with a calculator.

The start is about 103.92.

The answer is about 103.92 too.

So it is right!

Let's look back.

First: multiply.

Then: simplify the root.

Last: check.