Square root of 112
√112 ≈ 10.583. The square root of 112 is about 10.583, which simplifies to 4√7. 112 is not a perfect square, so √112 is irrational: its decimals never end or repeat.
| Value | 10.58300524 |
|---|---|
| Rounded | 10.6 (1 dp) · 10.58 (2 dp) · 10.583 (3 dp) |
| Simplest radical form | 4√7 |
| Perfect square? | No — between 10² = 100 and 11² = 121 |
| 112 squared | 12,544 |
Estimating √112 in your head
Start from the nearest perfect square, 11² = 121. 112 is 9 less than that. Divide the difference by twice the root, 22, and subtract it:
√112 ≈ 11 − 9 ÷ 22 ≈ 10.591
The true value is 10.583, so the one-step estimate is off by about 0.008. The estimate always comes out slightly high, and it is closest when 112 is near a perfect square. The method is explained in estimating square roots in your head.
Simplifying √112
Find the largest perfect square that divides 112: it is 16, since 112 = 16 × 7. Take its root outside: √112 = √16 × √7 = 4√7.
Frequently asked questions
What is the square root of 112?
The square root of 112 is about 10.583, which simplifies to 4√7. 112 is not a perfect square, so √112 is irrational: its decimals never end or repeat.
Is 112 a perfect square?
No. It lies between 10² = 100 and 11² = 121.
What is √112 in simplest radical form?
√112 = √(16 × 7) = 4√7.
Practise estimating square rootsNearby: √111 · √113 · all square roots to 150