Square root of 72
√72 ≈ 8.4853. The square root of 72 is about 8.4853, which simplifies to 6√2. 72 is not a perfect square, so √72 is irrational: its decimals never end or repeat.
| Value | 8.48528137 |
|---|---|
| Rounded | 8.5 (1 dp) · 8.49 (2 dp) · 8.485 (3 dp) |
| Simplest radical form | 6√2 |
| Perfect square? | No — between 8² = 64 and 9² = 81 |
| 72 squared | 5,184 |
Estimating √72 in your head
Start from the nearest perfect square, 8² = 64. 72 is 8 more than that. Divide the difference by twice the root, 16, and add it:
√72 ≈ 8 + 8 ÷ 16 ≈ 8.5
The true value is 8.4853, so the one-step estimate is off by about 0.015. The estimate always comes out slightly high, and it is closest when 72 is near a perfect square. The method is explained in estimating square roots in your head.
Simplifying √72
Find the largest perfect square that divides 72: it is 36, since 72 = 36 × 2. Take its root outside: √72 = √36 × √2 = 6√2.
Frequently asked questions
What is the square root of 72?
The square root of 72 is about 8.4853, which simplifies to 6√2. 72 is not a perfect square, so √72 is irrational: its decimals never end or repeat.
Is 72 a perfect square?
No. It lies between 8² = 64 and 9² = 81.
What is √72 in simplest radical form?
√72 = √(36 × 2) = 6√2.
Practise estimating square rootsNearby: √71 · √73 · all square roots to 150