Square root of 68
√68 ≈ 8.2462. The square root of 68 is about 8.2462, which simplifies to 2√17. 68 is not a perfect square, so √68 is irrational: its decimals never end or repeat.
| Value | 8.24621125 |
|---|---|
| Rounded | 8.2 (1 dp) · 8.25 (2 dp) · 8.246 (3 dp) |
| Simplest radical form | 2√17 |
| Perfect square? | No — between 8² = 64 and 9² = 81 |
| 68 squared | 4,624 |
Estimating √68 in your head
Start from the nearest perfect square, 8² = 64. 68 is 4 more than that. Divide the difference by twice the root, 16, and add it:
√68 ≈ 8 + 4 ÷ 16 ≈ 8.25
The true value is 8.2462, so the one-step estimate is off by about 0.004. The estimate always comes out slightly high, and it is closest when 68 is near a perfect square. The method is explained in estimating square roots in your head.
Simplifying √68
Find the largest perfect square that divides 68: it is 4, since 68 = 4 × 17. Take its root outside: √68 = √4 × √17 = 2√17.
Frequently asked questions
What is the square root of 68?
The square root of 68 is about 8.2462, which simplifies to 2√17. 68 is not a perfect square, so √68 is irrational: its decimals never end or repeat.
Is 68 a perfect square?
No. It lies between 8² = 64 and 9² = 81.
What is √68 in simplest radical form?
√68 = √(4 × 17) = 2√17.
Practise estimating square rootsNearby: √67 · √69 · all square roots to 150