Square root of 78
√78 ≈ 8.8318. The square root of 78 is about 8.8318. 78 is not a perfect square, so √78 is irrational: its decimals never end or repeat.
| Value | 8.83176087 |
|---|---|
| Rounded | 8.8 (1 dp) · 8.83 (2 dp) · 8.832 (3 dp) |
| Simplest radical form | √78 |
| Perfect square? | No — between 8² = 64 and 9² = 81 |
| 78 squared | 6,084 |
Estimating √78 in your head
Start from the nearest perfect square, 9² = 81. 78 is 3 less than that. Divide the difference by twice the root, 18, and subtract it:
√78 ≈ 9 − 3 ÷ 18 ≈ 8.833
The true value is 8.8318, so the one-step estimate is off by about 0.002. The estimate always comes out slightly high, and it is closest when 78 is near a perfect square. The method is explained in estimating square roots in your head.
Can √78 be simplified?
No. 78 has no perfect-square factor besides 1, so √78 is already in simplest radical form.
Frequently asked questions
What is the square root of 78?
The square root of 78 is about 8.8318. 78 is not a perfect square, so √78 is irrational: its decimals never end or repeat.
Is 78 a perfect square?
No. It lies between 8² = 64 and 9² = 81.
What is √78 in simplest radical form?
√78 is already in simplest form: 78 has no square factor other than 1.
Practise estimating square rootsNearby: √77 · √79 · all square roots to 150