Estimate √35 to the nearest tenth Step by Step

Step by step

The question

Question: estimate √35 to the nearest tenth.

√35

The square root of 35 is the number that times itself makes 35.

√35 × √35 = 35

Careful!

The square root is not half.

17.5 times 17.5 is 306.25, far more than 35.

Careful: not √35 = 17.5 ✗

1 List the squares

First, the square numbers near 35.

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

35 is between the squares 25 and 36.

= 25 < 35 < 36

A bigger number has a bigger square root.

So √35 is between √25 and √36.

= √25 < √35 < √36

√25 is 5.

√36 is 6.

So √35 is between 5 and 6.

= 5 < √35 < 6

3 Which is closer

35 is 10 more than 25, and 1 less than 36.

= 35 − 25 = 10, 36 − 35 = 1

1 is less.

So 35 is closer to 36, and √35 is closer to 6.

1 < 10: closer to 36

4 Try tenths

√35 is a bit less than 6.

So we try 5.9 and so on, and square each one.

5.9 times 5.9 is 34.81.

That is less than 35: too small.

= 5.9 × 5.9 = 34.81 → too small

So √35 is between 5.9 and 6.0.

= 5.9 < √35 < 6.0

5 Pick the nearest tenth

35 is 0.19 more than 34.81, and 1 less than 36.

So it is closer to 34.81.

= 35 − 34.81 = 0.19, 36 − 35 = 1

0.19 < 1: closer to 5.9

So √35 is about 5.9, to the nearest tenth.

= √35 ≈ 5.9

6 Check

Let's check with the number halfway: 5.95.

5.95 times 5.95 is 35.4025, more than 35.

5.95 × 5.95 = 35.4025 > 35

So √35 is below 5.95.

To the nearest tenth, it is 5.9.

The answer is right!

√35 < 5.95: nearest tenth 5.9

Let's look back.

First: list the squares.

Then: find where it fits.

Then: which is closer.

Then: try tenths.

Then: pick the nearest tenth.

Last: check.

Answer