Estimate √26 to the nearest tenth Step by Step

Step by step

The question

Question: estimate √26 to the nearest tenth.

√26

The square root of 26 is the number that times itself makes 26.

√26 × √26 = 26

Careful!

The square root is not half.

13 times 13 is 169, far more than 26.

Careful: not √26 = 13 ✗

1 List the squares

First, the square numbers near 26.

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

26 is between the squares 25 and 36.

= 25 < 26 < 36

A bigger number has a bigger square root.

So √26 is between √25 and √36.

= √25 < √26 < √36

√25 is 5.

√36 is 6.

So √26 is between 5 and 6.

= 5 < √26 < 6

3 Which is closer

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

= 26 − 25 = 1, 36 − 26 = 10

1 is less.

So 26 is closer to 25, and √26 is closer to 5.

1 < 10: closer to 25

4 Try tenths

√26 is a bit more than 5.

So we try 5.1 and so on, and square each one.

5.1 times 5.1 is 26.01.

That is more than 26: too big.

= 5.1 × 5.1 = 26.01 → too big

So √26 is between 5.0 and 5.1.

= 5.0 < √26 < 5.1

5 Pick the nearest tenth

26 is 1 more than 25, and 0.01 less than 26.01.

So it is closer to 26.01.

= 26 − 25 = 1, 26.01 − 26 = 0.01

0.01 < 1: closer to 5.1

So √26 is about 5.1, to the nearest tenth.

= √26 ≈ 5.1

6 Check

Let's check with the number halfway: 5.05.

5.05 times 5.05 is 25.5025, less than 26.

5.05 × 5.05 = 25.5025 < 26

So √26 is above 5.05.

To the nearest tenth, it is 5.1.

The answer is right!

√26 > 5.05: nearest tenth 5.1

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