Simplify 2√3 × 5√6

Step by step

The question

Question: work out 2√3 × 5√6.

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 5 is 10.

So it is 10 times the root of 3 times 6.

Careful!

This works for times, not for plus.

√9 + √16 is 3 + 4 = 7, but √25 is 5.

3 times 6 is 18.

2 Simplify the root

Now we make √18 simpler, like in the lesson on square roots.

The biggest square that goes into 18 is 9: 18 divided by 9 is 2.

So √18 is √9 times √2.

√9 is 3, because 3 times 3 is 9.

10 times 3 is 30.

So we get 30√2.

So 2√3 × 5√6 = 30√2.

3 Check

Let's check with a calculator.

The start is about 42.43.

The answer is about 42.43 too.

So it is right!

Let's look back.

First: multiply.

Then: simplify the root.

Last: check.