Estimate √50 to the nearest tenth Step by Step

Step by step

The question

Question: estimate √50 to the nearest tenth.

√50

The square root of 50 is the number that times itself makes 50.

√50 × √50 = 50

Careful!

The square root is not half.

25 times 25 is 625, far more than 50.

Careful: not √50 = 25 ✗

1 List the squares

First, the square numbers near 50.

6 times 6 is 36.

7 times 7 is 49.

8 times 8 is 64.

9 times 9 is 81.

2 Find where it fits

50 is between the squares 49 and 64.

= 49 < 50 < 64

A bigger number has a bigger square root.

So √50 is between √49 and √64.

= √49 < √50 < √64

√49 is 7.

√64 is 8.

So √50 is between 7 and 8.

= 7 < √50 < 8

3 Which is closer

50 is 1 more than 49, and 14 less than 64.

= 50 − 49 = 1, 64 − 50 = 14

1 is less.

So 50 is closer to 49, and √50 is closer to 7.

1 < 14: closer to 49

4 Try tenths

√50 is a bit more than 7.

So we try 7.1 and so on, and square each one.

7.1 times 7.1 is 50.41.

That is more than 50: too big.

= 7.1 × 7.1 = 50.41 → too big

So √50 is between 7.0 and 7.1.

= 7.0 < √50 < 7.1

5 Pick the nearest tenth

50 is 1 more than 49, and 0.41 less than 50.41.

So it is closer to 50.41.

= 50 − 49 = 1, 50.41 − 50 = 0.41

0.41 < 1: closer to 7.1

So √50 is about 7.1, to the nearest tenth.

= √50 ≈ 7.1

6 Check

Let's check with the number halfway: 7.05.

7.05 times 7.05 is 49.7025, less than 50.

7.05 × 7.05 = 49.7025 < 50

So √50 is above 7.05.

To the nearest tenth, it is 7.1.

The answer is right!

√50 > 7.05: nearest tenth 7.1

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