Square root of 59
√59 ≈ 7.6811. The square root of 59 is about 7.6811. 59 is not a perfect square, so √59 is irrational: its decimals never end or repeat.
| Value | 7.68114575 |
|---|---|
| Rounded | 7.7 (1 dp) · 7.68 (2 dp) · 7.681 (3 dp) |
| Simplest radical form | √59 |
| Perfect square? | No — between 7² = 49 and 8² = 64 |
| 59 squared | 3,481 |
Estimating √59 in your head
Start from the nearest perfect square, 8² = 64. 59 is 5 less than that. Divide the difference by twice the root, 16, and subtract it:
√59 ≈ 8 − 5 ÷ 16 ≈ 7.688
The true value is 7.6811, so the one-step estimate is off by about 0.006. The estimate always comes out slightly high, and it is closest when 59 is near a perfect square. The method is explained in estimating square roots in your head.
Can √59 be simplified?
No. 59 has no perfect-square factor besides 1, so √59 is already in simplest radical form.
Frequently asked questions
What is the square root of 59?
The square root of 59 is about 7.6811. 59 is not a perfect square, so √59 is irrational: its decimals never end or repeat.
Is 59 a perfect square?
No. It lies between 7² = 49 and 8² = 64.
What is √59 in simplest radical form?
√59 is already in simplest form: 59 has no square factor other than 1.
Practise estimating square rootsNearby: √58 · √60 · all square roots to 150