Square root of 17
√17 ≈ 4.1231. The square root of 17 is about 4.1231. 17 is not a perfect square, so √17 is irrational: its decimals never end or repeat.
| Value | 4.12310563 |
|---|---|
| Rounded | 4.1 (1 dp) · 4.12 (2 dp) · 4.123 (3 dp) |
| Simplest radical form | √17 |
| Perfect square? | No — between 4² = 16 and 5² = 25 |
| 17 squared | 289 |
Estimating √17 in your head
Start from the nearest perfect square, 4² = 16. 17 is 1 more than that. Divide the difference by twice the root, 8, and add it:
√17 ≈ 4 + 1 ÷ 8 ≈ 4.125
The true value is 4.1231, so the one-step estimate is off by about 0.002. The estimate always comes out slightly high, and it is closest when 17 is near a perfect square. The method is explained in estimating square roots in your head.
Can √17 be simplified?
No. 17 has no perfect-square factor besides 1, so √17 is already in simplest radical form.
Frequently asked questions
What is the square root of 17?
The square root of 17 is about 4.1231. 17 is not a perfect square, so √17 is irrational: its decimals never end or repeat.
Is 17 a perfect square?
No. It lies between 4² = 16 and 5² = 25.
What is √17 in simplest radical form?
√17 is already in simplest form: 17 has no square factor other than 1.
Practise estimating square rootsNearby: √16 · √18 · all square roots to 150