Step by step
The question
Question: find the radius r of a circle with area 25π square units.
1 Write the rule
The area of a circle is π times the radius squared: A = π × r².
Now put the numbers in: A = 25π.
Careful!
25 is r², the radius times itself.
We still need its square root.
2 Remove the π
π is on both sides.
So we divide both sides by π.
We do it on both sides.
Why both sides?
The = sign means both sides are the same amount.
If we change only one side, they are not the same any more.
π divided by π is 1.
So r² = 25.
3 Take the square root
r times r is 25.
So r is the square root of 25.
The square root of 25 is the positive number that times itself makes 25.
5 times 5 is 25.
So the radius is 5.
4 Check
Let's check: put r = 5 back in the rule.
We get 25π again.
So the radius is right!
Let's look back.
First: write the rule.
Then: remove the π.
Then: take the square root.
Last: check.