Square root of 132
√132 ≈ 11.4891. The square root of 132 is about 11.4891, which simplifies to 2√33. 132 is not a perfect square, so √132 is irrational: its decimals never end or repeat.
| Value | 11.48912529 |
|---|---|
| Rounded | 11.5 (1 dp) · 11.49 (2 dp) · 11.489 (3 dp) |
| Simplest radical form | 2√33 |
| Perfect square? | No — between 11² = 121 and 12² = 144 |
| 132 squared | 17,424 |
Estimating √132 in your head
Start from the nearest perfect square, 11² = 121. 132 is 11 more than that. Divide the difference by twice the root, 22, and add it:
√132 ≈ 11 + 11 ÷ 22 ≈ 11.5
The true value is 11.4891, so the one-step estimate is off by about 0.011. The estimate always comes out slightly high, and it is closest when 132 is near a perfect square. The method is explained in estimating square roots in your head.
Simplifying √132
Find the largest perfect square that divides 132: it is 4, since 132 = 4 × 33. Take its root outside: √132 = √4 × √33 = 2√33.
Frequently asked questions
What is the square root of 132?
The square root of 132 is about 11.4891, which simplifies to 2√33. 132 is not a perfect square, so √132 is irrational: its decimals never end or repeat.
Is 132 a perfect square?
No. It lies between 11² = 121 and 12² = 144.
What is √132 in simplest radical form?
√132 = √(4 × 33) = 2√33.
Practise estimating square rootsNearby: √131 · √133 · all square roots to 150