Simplify √11 × √33

Step by step

The question

Question: work out √11 × √33.

1 Multiply

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

So it is the root of 11 times 33.

Careful!

This works for times, not for plus.

√9 + √16 is 3 + 4 = 7, but √25 is 5.

11 times 33 is 363.

2 Simplify the root

Now we make √363 simpler, like in the lesson on square roots.

169 does not go into 363.

144 does not go into 363.

The biggest square that goes into 363 is 121: 363 divided by 121 is 3.

So √363 is √121 times √3.

√121 is 11, because 11 times 11 is 121.

So we get 11√3.

So √11 × √33 = 11√3.

3 Check

Let's check with a calculator.

The start is about 19.05.

The answer is about 19.05 too.

So it is right!

Let's look back.

First: multiply.

Then: simplify the root.

Last: check.