Step by step
The question
Question: simplify 4√8 − 2√18.
1 Find a square number in each
Square numbers are a number times itself: 2 × 2 = 4, 3 × 3 = 9, and so on.
We list them up to half of 18.
A bigger one can't go in.
First 8.
We try the biggest first.
Does 4 go into 8?
Yes: 8 divided by 4 is 2.
Now 18.
Does 9 go into 18?
Yes: 18 divided by 9 is 2.
2 Split each root
We write each number as the square times what is left.
Rule: a root over a times can be split into two roots.
So each root becomes two roots, times.
√4 is 2, because 2 times 2 is 4.
√9 is 3, because 3 times 3 is 9.
We write the numbers in place of the square roots.
4 times 2 is 8.
2 times 3 is 6.
We leave out the times sign: 8√2 means 8 times √2.
3 Put like roots together
They all have √2.
They are like terms, like 8 and 6 of the same thing.
8 minus 6 is 2.
So 4√8 − 2√18 = 2√2.
4 Check
Let's check with a calculator.
The start is about 2.83.
The answer is about 2.83 too.
So it is right!
Let's look back.
First: find a square number in each.
Then: split each root.
Then: put like roots together.
Last: check.