Square root of 150
√150 ≈ 12.2474. The square root of 150 is about 12.2474, which simplifies to 5√6. 150 is not a perfect square, so √150 is irrational: its decimals never end or repeat.
| Value | 12.24744871 |
|---|---|
| Rounded | 12.2 (1 dp) · 12.25 (2 dp) · 12.247 (3 dp) |
| Simplest radical form | 5√6 |
| Perfect square? | No — between 12² = 144 and 13² = 169 |
| 150 squared | 22,500 |
Estimating √150 in your head
Start from the nearest perfect square, 12² = 144. 150 is 6 more than that. Divide the difference by twice the root, 24, and add it:
√150 ≈ 12 + 6 ÷ 24 ≈ 12.25
The true value is 12.2474, so the one-step estimate is off by about 0.003. The estimate always comes out slightly high, and it is closest when 150 is near a perfect square. The method is explained in estimating square roots in your head.
Simplifying √150
Find the largest perfect square that divides 150: it is 25, since 150 = 25 × 6. Take its root outside: √150 = √25 × √6 = 5√6.
Frequently asked questions
What is the square root of 150?
The square root of 150 is about 12.2474, which simplifies to 5√6. 150 is not a perfect square, so √150 is irrational: its decimals never end or repeat.
Is 150 a perfect square?
No. It lies between 12² = 144 and 13² = 169.
What is √150 in simplest radical form?
√150 = √(25 × 6) = 5√6.
Practise estimating square rootsNearby: √149 · all square roots to 150