Square roots·√40
√40 =
2√10
≈ 6.324555

Square root of 40 — 6.324555 (2√10)

Irrational

The square root of 40 is about 6.324555, or exactly 2√10. It lies between 6 and 7.

As a decimal
≈ 6.324555
Simplified surd
√40 = 2√10
Between
6 < √40 < 7
Squared
40² = 1600
Cube root
∛40 ≈ 3.419952

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.

√40 = √(4 × 10) = 2√10

Nearby numbers

√37 = √37√38 = √38√39 = √39√41 = √41√42 = √42√43 = √43

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 40?

About 6.324555, or exactly 2√10.

Q. Can the surd be simplified?

Yes: 40 = 4 × 10, so 2 comes out and it becomes 2√10.

Q. Between which integers does it fall?

Between 6 and 7.

Q. What is the cube root of 40?

About 3.419952.