Square root of 8
√8 is about 2.828. It is not a whole number, and here is why.
The answer
The square root of 8 is about 2.828. It is between 2 and 3, because 4 < 8 < 9.
A note about this topic
England’s Year 5 curriculum includes recognising square numbers. The square-root explanations on this page are extension material.
8 drawn as a square
8 counters will not make a square. 4 of them make a 2 by 2 square, and 4 are left over. A 3 by 3 square needs 1 more. So the side, √8, is more than 2 but less than 3.
Between 2 and 3
4 < 8 < 9, so 2 < √8 < 3
2 × 2 = 4, which is too small, and 3 × 3 = 9, which is too big. So √8 is between 2 and 3. 8 is 4 away from 4 and 1 away from 9, so √8 is nearer 3. It is about 2.828, or 2.83 to 2 decimal places.
Why the decimal never ends
Check the answer by multiplying it by itself: 2.828 × 2.828 = 7.997584. That is very close to 8, but not quite. Adding more decimal places gets closer and closer, but never exactly there.
√8 is an irrational number: its digits go on forever without a repeating pattern, so no fraction is exactly equal to it. That is why we write √8 for the exact value and 2.828 when we need a number to work with.
√8 is exactly double √2, because 8 = 4 × 2 and √4 = 2. So √8 = 2 × 1.41421… = 2.828 to 3 decimal places.
Where √8 turns up
- The diagonal of a square with sides 2 cm long is exactly √8 cm, about 2.83 cm. That is twice the diagonal of a square with 1 cm sides, which is √2 cm.
Square numbers and their roots
The square numbers up to 144 are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144.
More numbers
See every factor of 8 or check whether 8 is prime.
Questions parents ask
What is √8 to 1 decimal place, and to 5?
2.8 to 1 decimal place, and 2.82843 to 5 decimal places.
A square has an area of 8 cm². How long is each side?
About 2.83 cm. The exact mathematical length is √8 cm. Use an approximation for a measurement.
Can a square root be negative?
Yes. −√8 × −√8 also makes 8, so −√8 is a square root of 8 too. For a positive number, the symbol √ denotes the positive root, √8. The negative root also gives 8 when multiplied by itself.
Continue your number practice
Explore the diagnostic for another set of practice questions.