Square root of 76
√76 ≈ 8.7178. The square root of 76 is about 8.7178, which simplifies to 2√19. 76 is not a perfect square, so √76 is irrational: its decimals never end or repeat.
| Value | 8.71779789 |
|---|---|
| Rounded | 8.7 (1 dp) · 8.72 (2 dp) · 8.718 (3 dp) |
| Simplest radical form | 2√19 |
| Perfect square? | No — between 8² = 64 and 9² = 81 |
| 76 squared | 5,776 |
Estimating √76 in your head
Start from the nearest perfect square, 9² = 81. 76 is 5 less than that. Divide the difference by twice the root, 18, and subtract it:
√76 ≈ 9 − 5 ÷ 18 ≈ 8.722
The true value is 8.7178, so the one-step estimate is off by about 0.004. The estimate always comes out slightly high, and it is closest when 76 is near a perfect square. The method is explained in estimating square roots in your head.
Simplifying √76
Find the largest perfect square that divides 76: it is 4, since 76 = 4 × 19. Take its root outside: √76 = √4 × √19 = 2√19.
Frequently asked questions
What is the square root of 76?
The square root of 76 is about 8.7178, which simplifies to 2√19. 76 is not a perfect square, so √76 is irrational: its decimals never end or repeat.
Is 76 a perfect square?
No. It lies between 8² = 64 and 9² = 81.
What is √76 in simplest radical form?
√76 = √(4 × 19) = 2√19.
Practise estimating square rootsNearby: √75 · √77 · all square roots to 150