Step by step
The question
Question: find the radius r of a circle with area 50.24 square units.
1 Write the rule
The area of a circle is π times the radius squared: A = π × r².
π is a special number for circles.
It is about 3.14.
Now put the numbers in: A = 50.24 and 3.14 for π.
Careful!
50.24 divided by 3.14 is r², the radius times itself.
We still need its square root.
2 Remove the × 3.14
We want r² by itself.
The times 3.14 is in the way.
To remove times 3.14, we divide by 3.14.
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.
3.14 divided by 3.14 is 1.
So just r² is left.
Check the division: 3.14 times 16 is 50.24.
50.24 divided by 3.14 is 16.
So r² = 16.
3 Take the square root
r times r is 16.
So r is the square root of 16.
The square root of 16 is the positive number that times itself makes 16.
4 times 4 is 16.
So the radius is 4.
4 Check
Let's check: put r = 4 back in the rule.
We get 50.24 again.
So the radius is right!
Let's look back.
First: write the rule.
Then: remove the × 3.14.
Then: take the square root.
Last: check.