Square root of 104
√104 ≈ 10.198. The square root of 104 is about 10.198, which simplifies to 2√26. 104 is not a perfect square, so √104 is irrational: its decimals never end or repeat.
| Value | 10.19803903 |
|---|---|
| Rounded | 10.2 (1 dp) · 10.20 (2 dp) · 10.198 (3 dp) |
| Simplest radical form | 2√26 |
| Perfect square? | No — between 10² = 100 and 11² = 121 |
| 104 squared | 10,816 |
Estimating √104 in your head
Start from the nearest perfect square, 10² = 100. 104 is 4 more than that. Divide the difference by twice the root, 20, and add it:
√104 ≈ 10 + 4 ÷ 20 ≈ 10.2
The true value is 10.198, so the one-step estimate is off by about 0.002. The estimate always comes out slightly high, and it is closest when 104 is near a perfect square. The method is explained in estimating square roots in your head.
Simplifying √104
Find the largest perfect square that divides 104: it is 4, since 104 = 4 × 26. Take its root outside: √104 = √4 × √26 = 2√26.
Frequently asked questions
What is the square root of 104?
The square root of 104 is about 10.198, which simplifies to 2√26. 104 is not a perfect square, so √104 is irrational: its decimals never end or repeat.
Is 104 a perfect square?
No. It lies between 10² = 100 and 11² = 121.
What is √104 in simplest radical form?
√104 = √(4 × 26) = 2√26.
Practise estimating square rootsNearby: √103 · √105 · all square roots to 150