Square root of 102
√102 ≈ 10.0995. The square root of 102 is about 10.0995. 102 is not a perfect square, so √102 is irrational: its decimals never end or repeat.
| Value | 10.09950494 |
|---|---|
| Rounded | 10.1 (1 dp) · 10.10 (2 dp) · 10.100 (3 dp) |
| Simplest radical form | √102 |
| Perfect square? | No — between 10² = 100 and 11² = 121 |
| 102 squared | 10,404 |
Estimating √102 in your head
Start from the nearest perfect square, 10² = 100. 102 is 2 more than that. Divide the difference by twice the root, 20, and add it:
√102 ≈ 10 + 2 ÷ 20 ≈ 10.1
The true value is 10.0995, so the one-step estimate is off by less than 0.001. The estimate always comes out slightly high, and it is closest when 102 is near a perfect square. The method is explained in estimating square roots in your head.
Can √102 be simplified?
No. 102 has no perfect-square factor besides 1, so √102 is already in simplest radical form.
Frequently asked questions
What is the square root of 102?
The square root of 102 is about 10.0995. 102 is not a perfect square, so √102 is irrational: its decimals never end or repeat.
Is 102 a perfect square?
No. It lies between 10² = 100 and 11² = 121.
What is √102 in simplest radical form?
√102 is already in simplest form: 102 has no square factor other than 1.
Practise estimating square rootsNearby: √101 · √103 · all square roots to 150