Square root of 147
√147 ≈ 12.1244. The square root of 147 is about 12.1244, which simplifies to 7√3. 147 is not a perfect square, so √147 is irrational: its decimals never end or repeat.
| Value | 12.12435565 |
|---|---|
| Rounded | 12.1 (1 dp) · 12.12 (2 dp) · 12.124 (3 dp) |
| Simplest radical form | 7√3 |
| Perfect square? | No — between 12² = 144 and 13² = 169 |
| 147 squared | 21,609 |
Estimating √147 in your head
Start from the nearest perfect square, 12² = 144. 147 is 3 more than that. Divide the difference by twice the root, 24, and add it:
√147 ≈ 12 + 3 ÷ 24 ≈ 12.125
The true value is 12.1244, so the one-step estimate is off by less than 0.001. The estimate always comes out slightly high, and it is closest when 147 is near a perfect square. The method is explained in estimating square roots in your head.
Simplifying √147
Find the largest perfect square that divides 147: it is 49, since 147 = 49 × 3. Take its root outside: √147 = √49 × √3 = 7√3.
Frequently asked questions
What is the square root of 147?
The square root of 147 is about 12.1244, which simplifies to 7√3. 147 is not a perfect square, so √147 is irrational: its decimals never end or repeat.
Is 147 a perfect square?
No. It lies between 12² = 144 and 13² = 169.
What is √147 in simplest radical form?
√147 = √(49 × 3) = 7√3.
Practise estimating square rootsNearby: √146 · √148 · all square roots to 150