Square root of 32
√32 ≈ 5.6569. The square root of 32 is about 5.6569, which simplifies to 4√2. 32 is not a perfect square, so √32 is irrational: its decimals never end or repeat.
| Value | 5.65685425 |
|---|---|
| Rounded | 5.7 (1 dp) · 5.66 (2 dp) · 5.657 (3 dp) |
| Simplest radical form | 4√2 |
| Perfect square? | No — between 5² = 25 and 6² = 36 |
| 32 squared | 1,024 |
Estimating √32 in your head
Start from the nearest perfect square, 6² = 36. 32 is 4 less than that. Divide the difference by twice the root, 12, and subtract it:
√32 ≈ 6 − 4 ÷ 12 ≈ 5.667
The true value is 5.6569, so the one-step estimate is off by about 0.01. The estimate always comes out slightly high, and it is closest when 32 is near a perfect square. The method is explained in estimating square roots in your head.
Simplifying √32
Find the largest perfect square that divides 32: it is 16, since 32 = 16 × 2. Take its root outside: √32 = √16 × √2 = 4√2.
Frequently asked questions
What is the square root of 32?
The square root of 32 is about 5.6569, which simplifies to 4√2. 32 is not a perfect square, so √32 is irrational: its decimals never end or repeat.
Is 32 a perfect square?
No. It lies between 5² = 25 and 6² = 36.
What is √32 in simplest radical form?
√32 = √(16 × 2) = 4√2.
Practise estimating square rootsNearby: √31 · √33 · all square roots to 150