Square root of 74
√74 ≈ 8.6023. The square root of 74 is about 8.6023. 74 is not a perfect square, so √74 is irrational: its decimals never end or repeat.
| Value | 8.60232527 |
|---|---|
| Rounded | 8.6 (1 dp) · 8.60 (2 dp) · 8.602 (3 dp) |
| Simplest radical form | √74 |
| Perfect square? | No — between 8² = 64 and 9² = 81 |
| 74 squared | 5,476 |
Estimating √74 in your head
Start from the nearest perfect square, 9² = 81. 74 is 7 less than that. Divide the difference by twice the root, 18, and subtract it:
√74 ≈ 9 − 7 ÷ 18 ≈ 8.611
The true value is 8.6023, so the one-step estimate is off by about 0.009. The estimate always comes out slightly high, and it is closest when 74 is near a perfect square. The method is explained in estimating square roots in your head.
Can √74 be simplified?
No. 74 has no perfect-square factor besides 1, so √74 is already in simplest radical form.
Frequently asked questions
What is the square root of 74?
The square root of 74 is about 8.6023. 74 is not a perfect square, so √74 is irrational: its decimals never end or repeat.
Is 74 a perfect square?
No. It lies between 8² = 64 and 9² = 81.
What is √74 in simplest radical form?
√74 is already in simplest form: 74 has no square factor other than 1.
Practise estimating square rootsNearby: √73 · √75 · all square roots to 150