Square root of 56
√56 ≈ 7.4833. The square root of 56 is about 7.4833, which simplifies to 2√14. 56 is not a perfect square, so √56 is irrational: its decimals never end or repeat.
| Value | 7.48331477 |
|---|---|
| Rounded | 7.5 (1 dp) · 7.48 (2 dp) · 7.483 (3 dp) |
| Simplest radical form | 2√14 |
| Perfect square? | No — between 7² = 49 and 8² = 64 |
| 56 squared | 3,136 |
Estimating √56 in your head
Start from the nearest perfect square, 7² = 49. 56 is 7 more than that. Divide the difference by twice the root, 14, and add it:
√56 ≈ 7 + 7 ÷ 14 ≈ 7.5
The true value is 7.4833, so the one-step estimate is off by about 0.017. The estimate always comes out slightly high, and it is closest when 56 is near a perfect square. The method is explained in estimating square roots in your head.
Simplifying √56
Find the largest perfect square that divides 56: it is 4, since 56 = 4 × 14. Take its root outside: √56 = √4 × √14 = 2√14.
Frequently asked questions
What is the square root of 56?
The square root of 56 is about 7.4833, which simplifies to 2√14. 56 is not a perfect square, so √56 is irrational: its decimals never end or repeat.
Is 56 a perfect square?
No. It lies between 7² = 49 and 8² = 64.
What is √56 in simplest radical form?
√56 = √(4 × 14) = 2√14.
Practise estimating square rootsNearby: √55 · √57 · all square roots to 150