Simplify 2√14 × 3√7

Step by step

The question

Question: work out 2√14 × 3√7.

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 3 is 6.

So it is 6 times the root of 14 times 7.

Careful!

This works for times, not for plus.

√9 + √16 is 3 + 4 = 7, but √25 is 5.

14 times 7 is 98.

2 Simplify the root

Now we make √98 simpler, like in the lesson on square roots.

The biggest square that goes into 98 is 49: 98 divided by 49 is 2.

So √98 is √49 times √2.

√49 is 7, because 7 times 7 is 49.

6 times 7 is 42.

So we get 42√2.

So 2√14 × 3√7 = 42√2.

3 Check

Let's check with a calculator.

The start is about 59.40.

The answer is about 59.40 too.

So it is right!

Let's look back.

First: multiply.

Then: simplify the root.

Last: check.