Square root of 48
√48 ≈ 6.9282. The square root of 48 is about 6.9282, which simplifies to 4√3. 48 is not a perfect square, so √48 is irrational: its decimals never end or repeat.
| Value | 6.92820323 |
|---|---|
| Rounded | 6.9 (1 dp) · 6.93 (2 dp) · 6.928 (3 dp) |
| Simplest radical form | 4√3 |
| Perfect square? | No — between 6² = 36 and 7² = 49 |
| 48 squared | 2,304 |
Estimating √48 in your head
Start from the nearest perfect square, 7² = 49. 48 is 1 less than that. Divide the difference by twice the root, 14, and subtract it:
√48 ≈ 7 − 1 ÷ 14 ≈ 6.929
The true value is 6.9282, so the one-step estimate is off by less than 0.001. The estimate always comes out slightly high, and it is closest when 48 is near a perfect square. The method is explained in estimating square roots in your head.
Simplifying √48
Find the largest perfect square that divides 48: it is 16, since 48 = 16 × 3. Take its root outside: √48 = √16 × √3 = 4√3.
Frequently asked questions
What is the square root of 48?
The square root of 48 is about 6.9282, which simplifies to 4√3. 48 is not a perfect square, so √48 is irrational: its decimals never end or repeat.
Is 48 a perfect square?
No. It lies between 6² = 36 and 7² = 49.
What is √48 in simplest radical form?
√48 = √(16 × 3) = 4√3.
Practise estimating square rootsNearby: √47 · √49 · all square roots to 150