Simplify √8 × √10

Step by step

The question

Question: work out √8 × √10.

1 Multiply

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

So it is the root of 8 times 10.

Careful!

This works for times, not for plus.

√9 + √16 is 3 + 4 = 7, but √25 is 5.

8 times 10 is 80.

2 Simplify the root

Now we make √80 simpler, like in the lesson on square roots.

36 does not go into 80.

25 does not go into 80.

The biggest square that goes into 80 is 16: 80 divided by 16 is 5.

So √80 is √16 times √5.

√16 is 4, because 4 times 4 is 16.

So we get 4√5.

So √8 × √10 = 4√5.

3 Check

Let's check with a calculator.

The start is about 8.94.

The answer is about 8.94 too.

So it is right!

Let's look back.

First: multiply.

Then: simplify the root.

Last: check.