Square root of 77
√77 ≈ 8.775. The square root of 77 is about 8.775. 77 is not a perfect square, so √77 is irrational: its decimals never end or repeat.
| Value | 8.77496439 |
|---|---|
| Rounded | 8.8 (1 dp) · 8.77 (2 dp) · 8.775 (3 dp) |
| Simplest radical form | √77 |
| Perfect square? | No — between 8² = 64 and 9² = 81 |
| 77 squared | 5,929 |
Estimating √77 in your head
Start from the nearest perfect square, 9² = 81. 77 is 4 less than that. Divide the difference by twice the root, 18, and subtract it:
√77 ≈ 9 − 4 ÷ 18 ≈ 8.778
The true value is 8.775, so the one-step estimate is off by about 0.003. The estimate always comes out slightly high, and it is closest when 77 is near a perfect square. The method is explained in estimating square roots in your head.
Can √77 be simplified?
No. 77 has no perfect-square factor besides 1, so √77 is already in simplest radical form.
Frequently asked questions
What is the square root of 77?
The square root of 77 is about 8.775. 77 is not a perfect square, so √77 is irrational: its decimals never end or repeat.
Is 77 a perfect square?
No. It lies between 8² = 64 and 9² = 81.
What is √77 in simplest radical form?
√77 is already in simplest form: 77 has no square factor other than 1.
Practise estimating square rootsNearby: √76 · √78 · all square roots to 150