Square root of 71
√71 ≈ 8.4261. The square root of 71 is about 8.4261. 71 is not a perfect square, so √71 is irrational: its decimals never end or repeat.
| Value | 8.42614977 |
|---|---|
| Rounded | 8.4 (1 dp) · 8.43 (2 dp) · 8.426 (3 dp) |
| Simplest radical form | √71 |
| Perfect square? | No — between 8² = 64 and 9² = 81 |
| 71 squared | 5,041 |
Estimating √71 in your head
Start from the nearest perfect square, 8² = 64. 71 is 7 more than that. Divide the difference by twice the root, 16, and add it:
√71 ≈ 8 + 7 ÷ 16 ≈ 8.438
The true value is 8.4261, so the one-step estimate is off by about 0.011. The estimate always comes out slightly high, and it is closest when 71 is near a perfect square. The method is explained in estimating square roots in your head.
Can √71 be simplified?
No. 71 has no perfect-square factor besides 1, so √71 is already in simplest radical form.
Frequently asked questions
What is the square root of 71?
The square root of 71 is about 8.4261. 71 is not a perfect square, so √71 is irrational: its decimals never end or repeat.
Is 71 a perfect square?
No. It lies between 8² = 64 and 9² = 81.
What is √71 in simplest radical form?
√71 is already in simplest form: 71 has no square factor other than 1.
Practise estimating square rootsNearby: √70 · √72 · all square roots to 150