Square roots·√45
√45 =
3√5
≈ 6.708204

Square root of 45 — 6.708204 (3√5)

Irrational

The square root of 45 is about 6.708204, or exactly 3√5. It lies between 6 and 7.

As a decimal
≈ 6.708204
Simplified surd
√45 = 3√5
Between
6 < √45 < 7
Squared
45² = 2025
Cube root
∛45 ≈ 3.556893

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.

√45 = √(9 × 5) = 3√5

Nearby numbers

√42 = √42√43 = √43√44 = 2√11√46 = √46√47 = √47√48 = 4√3

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 45?

About 6.708204, or exactly 3√5.

Q. Can the surd be simplified?

Yes: 45 = 9 × 5, so 3 comes out and it becomes 3√5.

Q. Between which integers does it fall?

Between 6 and 7.

Q. What is the cube root of 45?

About 3.556893.