Estimate √80 to the nearest tenth Step by Step

Step by step

The question

Question: estimate √80 to the nearest tenth.

√80

The square root of 80 is the number that times itself makes 80.

√80 × √80 = 80

Careful!

The square root is not half.

40 times 40 is 1600, far more than 80.

Careful: not √80 = 40 ✗

1 List the squares

First, the square numbers near 80.

7 times 7 is 49.

8 times 8 is 64.

9 times 9 is 81.

10 times 10 is 100.

2 Find where it fits

80 is between the squares 64 and 81.

= 64 < 80 < 81

A bigger number has a bigger square root.

So √80 is between √64 and √81.

= √64 < √80 < √81

√64 is 8.

√81 is 9.

So √80 is between 8 and 9.

= 8 < √80 < 9

3 Which is closer

80 is 16 more than 64, and 1 less than 81.

= 80 − 64 = 16, 81 − 80 = 1

1 is less.

So 80 is closer to 81, and √80 is closer to 9.

1 < 16: closer to 81

4 Try tenths

√80 is a bit less than 9.

So we try 8.9 and so on, and square each one.

8.9 times 8.9 is 79.21.

That is less than 80: too small.

= 8.9 × 8.9 = 79.21 → too small

So √80 is between 8.9 and 9.0.

= 8.9 < √80 < 9.0

5 Pick the nearest tenth

80 is 0.79 more than 79.21, and 1 less than 81.

So it is closer to 79.21.

= 80 − 79.21 = 0.79, 81 − 80 = 1

0.79 < 1: closer to 8.9

So √80 is about 8.9, to the nearest tenth.

= √80 ≈ 8.9

6 Check

Let's check with the number halfway: 8.95.

8.95 times 8.95 is 80.1025, more than 80.

8.95 × 8.95 = 80.1025 > 80

So √80 is below 8.95.

To the nearest tenth, it is 8.9.

The answer is right!

√80 < 8.95: nearest tenth 8.9

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