Square root of 93
√93 ≈ 9.6437. The square root of 93 is about 9.6437. 93 is not a perfect square, so √93 is irrational: its decimals never end or repeat.
| Value | 9.64365076 |
|---|---|
| Rounded | 9.6 (1 dp) · 9.64 (2 dp) · 9.644 (3 dp) |
| Simplest radical form | √93 |
| Perfect square? | No — between 9² = 81 and 10² = 100 |
| 93 squared | 8,649 |
Estimating √93 in your head
Start from the nearest perfect square, 10² = 100. 93 is 7 less than that. Divide the difference by twice the root, 20, and subtract it:
√93 ≈ 10 − 7 ÷ 20 ≈ 9.65
The true value is 9.6437, so the one-step estimate is off by about 0.006. The estimate always comes out slightly high, and it is closest when 93 is near a perfect square. The method is explained in estimating square roots in your head.
Can √93 be simplified?
No. 93 has no perfect-square factor besides 1, so √93 is already in simplest radical form.
Frequently asked questions
What is the square root of 93?
The square root of 93 is about 9.6437. 93 is not a perfect square, so √93 is irrational: its decimals never end or repeat.
Is 93 a perfect square?
No. It lies between 9² = 81 and 10² = 100.
What is √93 in simplest radical form?
√93 is already in simplest form: 93 has no square factor other than 1.
Practise estimating square rootsNearby: √92 · √94 · all square roots to 150