Step by step
The question
Question: simplify √50 − √8.
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 50.
A bigger one can't go in.
First 50.
We try the biggest first.
Does 25 go into 50?
Yes: 50 divided by 25 is 2.
Now 8.
Does 4 go into 8?
Yes: 8 divided by 4 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.
√25 is 5, because 5 times 5 is 25.
√4 is 2, because 2 times 2 is 4.
We write the numbers in place of the square roots.
We leave out the times sign: 5√2 means 5 times √2.
Careful!
We can't add the numbers under the roots.
√9 + √16 is 3 + 4 = 7, not √25 = 5.
3 Put like roots together
They all have √2.
They are like terms, like 5 and 2 of the same thing.
5 minus 2 is 3.
So √50 − √8 = 3√2.
4 Check
Let's check with a calculator.
The start is about 4.24.
The answer is about 4.24 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.