Simplify 2√5 × √10

Step by step

The question

Question: work out 2√5 × √10.

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.

2 times 1 is 2.

So it is 2 times the root of 5 times 10.

Careful!

This works for times, not for plus.

√9 + √16 is 3 + 4 = 7, but √25 is 5.

5 times 10 is 50.

2 Simplify the root

Now we make √50 simpler, like in the lesson on square roots.

The biggest square that goes into 50 is 25: 50 divided by 25 is 2.

So √50 is √25 times √2.

√25 is 5, because 5 times 5 is 25.

2 times 5 is 10.

So we get 10√2.

So 2√5 × √10 = 10√2.

3 Check

Let's check with a calculator.

The start is about 14.14.

The answer is about 14.14 too.

So it is right!

Let's look back.

First: multiply.

Then: simplify the root.

Last: check.