Simplify √18 × √24

Step by step

The question

Question: work out √18 × √24.

1 Multiply

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

So it is the root of 18 times 24.

Careful!

This works for times, not for plus.

√9 + √16 is 3 + 4 = 7, but √25 is 5.

18 times 24 is 432.

2 Simplify the root

Now we make √432 simpler, like in the lesson on square roots.

196 does not go into 432.

169 does not go into 432.

The biggest square that goes into 432 is 144: 432 divided by 144 is 3.

So √432 is √144 times √3.

√144 is 12, because 12 times 12 is 144.

So we get 12√3.

So √18 × √24 = 12√3.

3 Check

Let's check with a calculator.

The start is about 20.78.

The answer is about 20.78 too.

So it is right!

Let's look back.

First: multiply.

Then: simplify the root.

Last: check.