Square root of 80
√80 ≈ 8.9443. The square root of 80 is about 8.9443, which simplifies to 4√5. 80 is not a perfect square, so √80 is irrational: its decimals never end or repeat.
| Value | 8.94427191 |
|---|---|
| Rounded | 8.9 (1 dp) · 8.94 (2 dp) · 8.944 (3 dp) |
| Simplest radical form | 4√5 |
| Perfect square? | No — between 8² = 64 and 9² = 81 |
| 80 squared | 6,400 |
Estimating √80 in your head
Start from the nearest perfect square, 9² = 81. 80 is 1 less than that. Divide the difference by twice the root, 18, and subtract it:
√80 ≈ 9 − 1 ÷ 18 ≈ 8.944
The true value is 8.9443, so the one-step estimate is off by less than 0.001. The estimate always comes out slightly high, and it is closest when 80 is near a perfect square. The method is explained in estimating square roots in your head.
Simplifying √80
Find the largest perfect square that divides 80: it is 16, since 80 = 16 × 5. Take its root outside: √80 = √16 × √5 = 4√5.
Frequently asked questions
What is the square root of 80?
The square root of 80 is about 8.9443, which simplifies to 4√5. 80 is not a perfect square, so √80 is irrational: its decimals never end or repeat.
Is 80 a perfect square?
No. It lies between 8² = 64 and 9² = 81.
What is √80 in simplest radical form?
√80 = √(16 × 5) = 4√5.
Practise estimating square rootsNearby: √79 · √81 · all square roots to 150