Estimate √30 Step by Step | Estimating square roots

Step by step

The question

Question: estimate √30.

√30

The square root of 30 is the number that times itself makes 30.

√30 × √30 = 30

Careful!

The square root is not half.

15 times 15 is 225, far more than 30.

Careful: not √30 = 15 ✗

1 List the squares

First, the square numbers near 30.

4 times 4 is 16.

5 times 5 is 25.

6 times 6 is 36.

7 times 7 is 49.

2 Find where it fits

30 is between the squares 25 and 36.

= 25 < 30 < 36

A bigger number has a bigger square root.

So √30 is between √25 and √36.

= √25 < √30 < √36

√25 is 5.

√36 is 6.

So √30 is between 5 and 6.

= 5 < √30 < 6

3 Which is closer

30 is 5 more than 25, and 6 less than 36.

= 30 − 25 = 5, 36 − 30 = 6

5 is less.

So 30 is closer to 25, and √30 is closer to 5.

5 < 6: closer to 25

So √30 is between 5 and 6, closer to 5.

= 5 < √30 < 6, closer to 5

4 Check

Let's check with the number halfway: 5.5.

5.5 times 5.5 is 30.25, more than 30.

5.5 × 5.5 = 30.25 > 30

So √30 is below 5.5: closer to 5.

The answer is right!

√30 < 5.5: closer to 5

Let's look back.

First: list the squares.

Then: find where it fits.

Then: which is closer.

Last: check.

Answer