Is √49 rational or irrational

Step by step

The question

Question: is √49 rational or irrational?

Rational means: it can be written as a fraction, with whole numbers on top and at the bottom.

Then its decimal stops, or repeats for ever.

Irrational means: no fraction works.

Its decimal never stops and never repeats.

1 Look for a square number

Square numbers are a number times itself.

6 times 6 is 36.

7 times 7 is 49.

8 times 8 is 64.

49 is a square number: 7 times 7.

So √49 is 7, a whole number.

7 is 7/1.

Careful!

A root sign does not always mean irrational.

√49 is just 7.

So √49 is rational.

It is a whole number.

2 Check

Let's check: 7 times 7 is 49.

So √49 really is 7.

So the answer is right!

Let's look back.

First: look for a square number.

Last: check.