Square root of 5
√5 ≈ 2.2361. The square root of 5 is about 2.2361. 5 is not a perfect square, so √5 is irrational: its decimals never end or repeat.
| Value | 2.23606798 |
|---|---|
| Rounded | 2.2 (1 dp) · 2.24 (2 dp) · 2.236 (3 dp) |
| Simplest radical form | √5 |
| Perfect square? | No — between 2² = 4 and 3² = 9 |
| 5 squared | 25 |
Estimating √5 in your head
Start from the nearest perfect square, 2² = 4. 5 is 1 more than that. Divide the difference by twice the root, 4, and add it:
√5 ≈ 2 + 1 ÷ 4 ≈ 2.25
The true value is 2.2361, so the one-step estimate is off by about 0.014. The estimate always comes out slightly high, and it is closest when 5 is near a perfect square. The method is explained in estimating square roots in your head.
Can √5 be simplified?
No. 5 has no perfect-square factor besides 1, so √5 is already in simplest radical form.
Frequently asked questions
What is the square root of 5?
The square root of 5 is about 2.2361. 5 is not a perfect square, so √5 is irrational: its decimals never end or repeat.
Is 5 a perfect square?
No. It lies between 2² = 4 and 3² = 9.
What is √5 in simplest radical form?
√5 is already in simplest form: 5 has no square factor other than 1.
Practise estimating square rootsNearby: √4 · √6 · all square roots to 150