Square root of 18
√18 ≈ 4.2426. The square root of 18 is about 4.2426, which simplifies to 3√2. 18 is not a perfect square, so √18 is irrational: its decimals never end or repeat.
| Value | 4.24264069 |
|---|---|
| Rounded | 4.2 (1 dp) · 4.24 (2 dp) · 4.243 (3 dp) |
| Simplest radical form | 3√2 |
| Perfect square? | No — between 4² = 16 and 5² = 25 |
| 18 squared | 324 |
Estimating √18 in your head
Start from the nearest perfect square, 4² = 16. 18 is 2 more than that. Divide the difference by twice the root, 8, and add it:
√18 ≈ 4 + 2 ÷ 8 ≈ 4.25
The true value is 4.2426, so the one-step estimate is off by about 0.007. The estimate always comes out slightly high, and it is closest when 18 is near a perfect square. The method is explained in estimating square roots in your head.
Simplifying √18
Find the largest perfect square that divides 18: it is 9, since 18 = 9 × 2. Take its root outside: √18 = √9 × √2 = 3√2.
Frequently asked questions
What is the square root of 18?
The square root of 18 is about 4.2426, which simplifies to 3√2. 18 is not a perfect square, so √18 is irrational: its decimals never end or repeat.
Is 18 a perfect square?
No. It lies between 4² = 16 and 5² = 25.
What is √18 in simplest radical form?
√18 = √(9 × 2) = 3√2.
Practise estimating square rootsNearby: √17 · √19 · all square roots to 150