Step by step
The question
Question: estimate √90.
The square root of 90 is the number that times itself makes 90.
Careful!
The square root is not half.
45 times 45 is 2025, far more than 90.
1 List the squares
First, the square numbers near 90.
8 times 8 is 64.
9 times 9 is 81.
10 times 10 is 100.
11 times 11 is 121.
2 Find where it fits
90 is between the squares 81 and 100.
A bigger number has a bigger square root.
So √90 is between √81 and √100.
√81 is 9.
√100 is 10.
So √90 is between 9 and 10.
3 Which is closer
90 is 9 more than 81, and 10 less than 100.
9 is less.
So 90 is closer to 81, and √90 is closer to 9.
So √90 is between 9 and 10, closer to 9.
4 Check
Let's check with the number halfway: 9.5.
9.5 times 9.5 is 90.25, more than 90.
So √90 is below 9.5: closer to 9.
The answer is right!
Let's look back.
First: list the squares.
Then: find where it fits.
Then: which is closer.
Last: check.