Square root of 60
√60 ≈ 7.746. The square root of 60 is about 7.746, which simplifies to 2√15. 60 is not a perfect square, so √60 is irrational: its decimals never end or repeat.
| Value | 7.74596669 |
|---|---|
| Rounded | 7.7 (1 dp) · 7.75 (2 dp) · 7.746 (3 dp) |
| Simplest radical form | 2√15 |
| Perfect square? | No — between 7² = 49 and 8² = 64 |
| 60 squared | 3,600 |
Estimating √60 in your head
Start from the nearest perfect square, 8² = 64. 60 is 4 less than that. Divide the difference by twice the root, 16, and subtract it:
√60 ≈ 8 − 4 ÷ 16 ≈ 7.75
The true value is 7.746, so the one-step estimate is off by about 0.004. The estimate always comes out slightly high, and it is closest when 60 is near a perfect square. The method is explained in estimating square roots in your head.
Simplifying √60
Find the largest perfect square that divides 60: it is 4, since 60 = 4 × 15. Take its root outside: √60 = √4 × √15 = 2√15.
Frequently asked questions
What is the square root of 60?
The square root of 60 is about 7.746, which simplifies to 2√15. 60 is not a perfect square, so √60 is irrational: its decimals never end or repeat.
Is 60 a perfect square?
No. It lies between 7² = 49 and 8² = 64.
What is √60 in simplest radical form?
√60 = √(4 × 15) = 2√15.
Practise estimating square rootsNearby: √59 · √61 · all square roots to 150