Square root of 61
√61 ≈ 7.8102. The square root of 61 is about 7.8102. 61 is not a perfect square, so √61 is irrational: its decimals never end or repeat.
| Value | 7.81024968 |
|---|---|
| Rounded | 7.8 (1 dp) · 7.81 (2 dp) · 7.810 (3 dp) |
| Simplest radical form | √61 |
| Perfect square? | No — between 7² = 49 and 8² = 64 |
| 61 squared | 3,721 |
Estimating √61 in your head
Start from the nearest perfect square, 8² = 64. 61 is 3 less than that. Divide the difference by twice the root, 16, and subtract it:
√61 ≈ 8 − 3 ÷ 16 ≈ 7.813
The true value is 7.8102, so the one-step estimate is off by about 0.002. The estimate always comes out slightly high, and it is closest when 61 is near a perfect square. The method is explained in estimating square roots in your head.
Can √61 be simplified?
No. 61 has no perfect-square factor besides 1, so √61 is already in simplest radical form.
Frequently asked questions
What is the square root of 61?
The square root of 61 is about 7.8102. 61 is not a perfect square, so √61 is irrational: its decimals never end or repeat.
Is 61 a perfect square?
No. It lies between 7² = 49 and 8² = 64.
What is √61 in simplest radical form?
√61 is already in simplest form: 61 has no square factor other than 1.
Practise estimating square rootsNearby: √60 · √62 · all square roots to 150