Square roots·√32
√32 =
4√2
≈ 5.656854

Square root of 32 — 5.656854 (4√2)

Irrational

The square root of 32 is about 5.656854, or exactly 4√2. It lies between 5 and 6.

As a decimal
≈ 5.656854
Simplified surd
√32 = 4√2
Between
5 < √32 < 6
Squared
32² = 1024
Cube root
∛32 ≈ 3.174802

How the surd is simplified

Pull out the largest square factor. Since 50 = 25 × 2, the root of 25 comes out as 5 and the 2 stays behind: 5√2.

√32 = √(16 × 2) = 4√2

Nearby numbers

√29 = √29√30 = √30√31 = √31√33 = √33√34 = √34√35 = √35

From 1 to 200

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How to read this

  • The decimal is rounded; the surd form is the exact value.
  • Pulling out a square factor simplifies the surd — √50 = 5√2.
  • If the number is not a perfect square, the decimal never ends (irrational).
  • Knowing which two integers it sits between is enough to estimate in your head.

Frequently asked questions

Q. What is the square root of 32?

About 5.656854, or exactly 4√2.

Q. Can the surd be simplified?

Yes: 32 = 16 × 2, so 4 comes out and it becomes 4√2.

Q. Between which integers does it fall?

Between 5 and 6.

Q. What is the cube root of 32?

About 3.174802.