Step by step
The question
Question: estimate √70.
The square root of 70 is the number that times itself makes 70.
Careful!
The square root is not half.
35 times 35 is 1225, far more than 70.
1 List the squares
First, the square numbers near 70.
7 times 7 is 49.
8 times 8 is 64.
9 times 9 is 81.
10 times 10 is 100.
2 Find where it fits
70 is between the squares 64 and 81.
A bigger number has a bigger square root.
So √70 is between √64 and √81.
√64 is 8.
√81 is 9.
So √70 is between 8 and 9.
3 Which is closer
70 is 6 more than 64, and 11 less than 81.
6 is less.
So 70 is closer to 64, and √70 is closer to 8.
So √70 is between 8 and 9, closer to 8.
4 Check
Let's check with the number halfway: 8.5.
8.5 times 8.5 is 72.25, more than 70.
So √70 is below 8.5: closer to 8.
The answer is right!
Let's look back.
First: list the squares.
Then: find where it fits.
Then: which is closer.
Last: check.