Square root of 101
√101 ≈ 10.0499. The square root of 101 is about 10.0499. 101 is not a perfect square, so √101 is irrational: its decimals never end or repeat.
| Value | 10.04987562 |
|---|---|
| Rounded | 10.0 (1 dp) · 10.05 (2 dp) · 10.050 (3 dp) |
| Simplest radical form | √101 |
| Perfect square? | No — between 10² = 100 and 11² = 121 |
| 101 squared | 10,201 |
Estimating √101 in your head
Start from the nearest perfect square, 10² = 100. 101 is 1 more than that. Divide the difference by twice the root, 20, and add it:
√101 ≈ 10 + 1 ÷ 20 ≈ 10.05
The true value is 10.0499, so the one-step estimate is off by less than 0.001. The estimate always comes out slightly high, and it is closest when 101 is near a perfect square. The method is explained in estimating square roots in your head.
Can √101 be simplified?
No. 101 has no perfect-square factor besides 1, so √101 is already in simplest radical form.
Frequently asked questions
What is the square root of 101?
The square root of 101 is about 10.0499. 101 is not a perfect square, so √101 is irrational: its decimals never end or repeat.
Is 101 a perfect square?
No. It lies between 10² = 100 and 11² = 121.
What is √101 in simplest radical form?
√101 is already in simplest form: 101 has no square factor other than 1.
Practise estimating square rootsNearby: √100 · √102 · all square roots to 150