Square root of 54
√54 ≈ 7.3485. The square root of 54 is about 7.3485, which simplifies to 3√6. 54 is not a perfect square, so √54 is irrational: its decimals never end or repeat.
| Value | 7.34846923 |
|---|---|
| Rounded | 7.3 (1 dp) · 7.35 (2 dp) · 7.348 (3 dp) |
| Simplest radical form | 3√6 |
| Perfect square? | No — between 7² = 49 and 8² = 64 |
| 54 squared | 2,916 |
Estimating √54 in your head
Start from the nearest perfect square, 7² = 49. 54 is 5 more than that. Divide the difference by twice the root, 14, and add it:
√54 ≈ 7 + 5 ÷ 14 ≈ 7.357
The true value is 7.3485, so the one-step estimate is off by about 0.009. The estimate always comes out slightly high, and it is closest when 54 is near a perfect square. The method is explained in estimating square roots in your head.
Simplifying √54
Find the largest perfect square that divides 54: it is 9, since 54 = 9 × 6. Take its root outside: √54 = √9 × √6 = 3√6.
Frequently asked questions
What is the square root of 54?
The square root of 54 is about 7.3485, which simplifies to 3√6. 54 is not a perfect square, so √54 is irrational: its decimals never end or repeat.
Is 54 a perfect square?
No. It lies between 7² = 49 and 8² = 64.
What is √54 in simplest radical form?
√54 = √(9 × 6) = 3√6.
Practise estimating square rootsNearby: √53 · √55 · all square roots to 150