Square root of 113
√113 ≈ 10.6301. The square root of 113 is about 10.6301. 113 is not a perfect square, so √113 is irrational: its decimals never end or repeat.
| Value | 10.63014581 |
|---|---|
| Rounded | 10.6 (1 dp) · 10.63 (2 dp) · 10.630 (3 dp) |
| Simplest radical form | √113 |
| Perfect square? | No — between 10² = 100 and 11² = 121 |
| 113 squared | 12,769 |
Estimating √113 in your head
Start from the nearest perfect square, 11² = 121. 113 is 8 less than that. Divide the difference by twice the root, 22, and subtract it:
√113 ≈ 11 − 8 ÷ 22 ≈ 10.636
The true value is 10.6301, so the one-step estimate is off by about 0.006. The estimate always comes out slightly high, and it is closest when 113 is near a perfect square. The method is explained in estimating square roots in your head.
Can √113 be simplified?
No. 113 has no perfect-square factor besides 1, so √113 is already in simplest radical form.
Frequently asked questions
What is the square root of 113?
The square root of 113 is about 10.6301. 113 is not a perfect square, so √113 is irrational: its decimals never end or repeat.
Is 113 a perfect square?
No. It lies between 10² = 100 and 11² = 121.
What is √113 in simplest radical form?
√113 is already in simplest form: 113 has no square factor other than 1.
Practise estimating square rootsNearby: √112 · √114 · all square roots to 150