Square root of 30
√30 ≈ 5.4772. The square root of 30 is about 5.4772. 30 is not a perfect square, so √30 is irrational: its decimals never end or repeat.
| Value | 5.47722558 |
|---|---|
| Rounded | 5.5 (1 dp) · 5.48 (2 dp) · 5.477 (3 dp) |
| Simplest radical form | √30 |
| Perfect square? | No — between 5² = 25 and 6² = 36 |
| 30 squared | 900 |
Estimating √30 in your head
Start from the nearest perfect square, 5² = 25. 30 is 5 more than that. Divide the difference by twice the root, 10, and add it:
√30 ≈ 5 + 5 ÷ 10 ≈ 5.5
The true value is 5.4772, so the one-step estimate is off by about 0.023. The estimate always comes out slightly high, and it is closest when 30 is near a perfect square. The method is explained in estimating square roots in your head.
Can √30 be simplified?
No. 30 has no perfect-square factor besides 1, so √30 is already in simplest radical form.
Frequently asked questions
What is the square root of 30?
The square root of 30 is about 5.4772. 30 is not a perfect square, so √30 is irrational: its decimals never end or repeat.
Is 30 a perfect square?
No. It lies between 5² = 25 and 6² = 36.
What is √30 in simplest radical form?
√30 is already in simplest form: 30 has no square factor other than 1.
Practise estimating square rootsNearby: √29 · √31 · all square roots to 150