Step by step
The question
Question: estimate √50.
The square root of 50 is the number that times itself makes 50.
Careful!
The square root is not half.
25 times 25 is 625, far more than 50.
1 List the squares
First, the square numbers near 50.
6 times 6 is 36.
7 times 7 is 49.
8 times 8 is 64.
9 times 9 is 81.
2 Find where it fits
50 is between the squares 49 and 64.
A bigger number has a bigger square root.
So √50 is between √49 and √64.
√49 is 7.
√64 is 8.
So √50 is between 7 and 8.
3 Which is closer
50 is 1 more than 49, and 14 less than 64.
1 is less.
So 50 is closer to 49, and √50 is closer to 7.
So √50 is between 7 and 8, closer to 7.
4 Check
Let's check with the number halfway: 7.5.
7.5 times 7.5 is 56.25, more than 50.
So √50 is below 7.5: closer to 7.
The answer is right!
Let's look back.
First: list the squares.
Then: find where it fits.
Then: which is closer.
Last: check.