Square root of 58
√58 ≈ 7.6158. The square root of 58 is about 7.6158. 58 is not a perfect square, so √58 is irrational: its decimals never end or repeat.
| Value | 7.61577311 |
|---|---|
| Rounded | 7.6 (1 dp) · 7.62 (2 dp) · 7.616 (3 dp) |
| Simplest radical form | √58 |
| Perfect square? | No — between 7² = 49 and 8² = 64 |
| 58 squared | 3,364 |
Estimating √58 in your head
Start from the nearest perfect square, 8² = 64. 58 is 6 less than that. Divide the difference by twice the root, 16, and subtract it:
√58 ≈ 8 − 6 ÷ 16 ≈ 7.625
The true value is 7.6158, so the one-step estimate is off by about 0.009. The estimate always comes out slightly high, and it is closest when 58 is near a perfect square. The method is explained in estimating square roots in your head.
Can √58 be simplified?
No. 58 has no perfect-square factor besides 1, so √58 is already in simplest radical form.
Frequently asked questions
What is the square root of 58?
The square root of 58 is about 7.6158. 58 is not a perfect square, so √58 is irrational: its decimals never end or repeat.
Is 58 a perfect square?
No. It lies between 7² = 49 and 8² = 64.
What is √58 in simplest radical form?
√58 is already in simplest form: 58 has no square factor other than 1.
Practise estimating square rootsNearby: √57 · √59 · all square roots to 150