√20 is between which two whole numbers Step by Step

Step by step

The question

Question: estimate √20.

√20

The square root of 20 is the number that times itself makes 20.

√20 × √20 = 20

Careful!

The square root is not half.

10 times 10 is 100, far more than 20.

Careful: not √20 = 10 ✗

1 List the squares

First, the square numbers near 20.

3 times 3 is 9.

4 times 4 is 16.

5 times 5 is 25.

6 times 6 is 36.

2 Find where it fits

20 is between the squares 16 and 25.

= 16 < 20 < 25

A bigger number has a bigger square root.

So √20 is between √16 and √25.

= √16 < √20 < √25

√16 is 4.

√25 is 5.

So √20 is between 4 and 5.

= 4 < √20 < 5

3 Which is closer

20 is 4 more than 16, and 5 less than 25.

= 20 − 16 = 4, 25 − 20 = 5

4 is less.

So 20 is closer to 16, and √20 is closer to 4.

4 < 5: closer to 16

So √20 is between 4 and 5, closer to 4.

= 4 < √20 < 5, closer to 4

4 Check

Let's check with the number halfway: 4.5.

4.5 times 4.5 is 20.25, more than 20.

4.5 × 4.5 = 20.25 > 20

So √20 is below 4.5: closer to 4.

The answer is right!

√20 < 4.5: closer to 4

Let's look back.

First: list the squares.

Then: find where it fits.

Then: which is closer.

Last: check.

Answer