Simplify √20 × √15

Step by step

The question

Question: work out √20 × √15.

1 Multiply

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

So it is the root of 20 times 15.

Careful!

This works for times, not for plus.

√9 + √16 is 3 + 4 = 7, but √25 is 5.

20 times 15 is 300.

2 Simplify the root

Now we make √300 simpler, like in the lesson on square roots.

144 does not go into 300.

121 does not go into 300.

The biggest square that goes into 300 is 100: 300 divided by 100 is 3.

So √300 is √100 times √3.

√100 is 10, because 10 times 10 is 100.

So we get 10√3.

So √20 × √15 = 10√3.

3 Check

Let's check with a calculator.

The start is about 17.32.

The answer is about 17.32 too.

So it is right!

Let's look back.

First: multiply.

Then: simplify the root.

Last: check.