Square root of 24
√24 ≈ 4.899. The square root of 24 is about 4.899, which simplifies to 2√6. 24 is not a perfect square, so √24 is irrational: its decimals never end or repeat.
| Value | 4.89897949 |
|---|---|
| Rounded | 4.9 (1 dp) · 4.90 (2 dp) · 4.899 (3 dp) |
| Simplest radical form | 2√6 |
| Perfect square? | No — between 4² = 16 and 5² = 25 |
| 24 squared | 576 |
Estimating √24 in your head
Start from the nearest perfect square, 5² = 25. 24 is 1 less than that. Divide the difference by twice the root, 10, and subtract it:
√24 ≈ 5 − 1 ÷ 10 ≈ 4.9
The true value is 4.899, so the one-step estimate is off by about 0.001. The estimate always comes out slightly high, and it is closest when 24 is near a perfect square. The method is explained in estimating square roots in your head.
Simplifying √24
Find the largest perfect square that divides 24: it is 4, since 24 = 4 × 6. Take its root outside: √24 = √4 × √6 = 2√6.
Frequently asked questions
What is the square root of 24?
The square root of 24 is about 4.899, which simplifies to 2√6. 24 is not a perfect square, so √24 is irrational: its decimals never end or repeat.
Is 24 a perfect square?
No. It lies between 4² = 16 and 5² = 25.
What is √24 in simplest radical form?
√24 = √(4 × 6) = 2√6.
Practise estimating square rootsNearby: √23 · √25 · all square roots to 150