Step by step
The question
Question: estimate √5.
The square root of 5 is the number that times itself makes 5.
Careful!
The square root is not half.
2.5 times 2.5 is 6.25, far more than 5.
1 List the squares
First, the square numbers near 5.
1 times 1 is 1.
2 times 2 is 4.
3 times 3 is 9.
4 times 4 is 16.
2 Find where it fits
5 is between the squares 4 and 9.
A bigger number has a bigger square root.
So √5 is between √4 and √9.
√4 is 2.
√9 is 3.
So √5 is between 2 and 3.
3 Which is closer
5 is 1 more than 4, and 4 less than 9.
1 is less.
So 5 is closer to 4, and √5 is closer to 2.
So √5 is between 2 and 3, closer to 2.
4 Check
Let's check with the number halfway: 2.5.
2.5 times 2.5 is 6.25, more than 5.
So √5 is below 2.5: closer to 2.
The answer is right!
Let's look back.
First: list the squares.
Then: find where it fits.
Then: which is closer.
Last: check.