Square root of 103
√103 ≈ 10.1489. The square root of 103 is about 10.1489. 103 is not a perfect square, so √103 is irrational: its decimals never end or repeat.
| Value | 10.14889157 |
|---|---|
| Rounded | 10.1 (1 dp) · 10.15 (2 dp) · 10.149 (3 dp) |
| Simplest radical form | √103 |
| Perfect square? | No — between 10² = 100 and 11² = 121 |
| 103 squared | 10,609 |
Estimating √103 in your head
Start from the nearest perfect square, 10² = 100. 103 is 3 more than that. Divide the difference by twice the root, 20, and add it:
√103 ≈ 10 + 3 ÷ 20 ≈ 10.15
The true value is 10.1489, so the one-step estimate is off by about 0.001. The estimate always comes out slightly high, and it is closest when 103 is near a perfect square. The method is explained in estimating square roots in your head.
Can √103 be simplified?
No. 103 has no perfect-square factor besides 1, so √103 is already in simplest radical form.
Frequently asked questions
What is the square root of 103?
The square root of 103 is about 10.1489. 103 is not a perfect square, so √103 is irrational: its decimals never end or repeat.
Is 103 a perfect square?
No. It lies between 10² = 100 and 11² = 121.
What is √103 in simplest radical form?
√103 is already in simplest form: 103 has no square factor other than 1.
Practise estimating square rootsNearby: √102 · √104 · all square roots to 150