Square roots·√90
√90 =
3√10
≈ 9.486833

Square root of 90 — 9.486833 (3√10)

Irrational

The square root of 90 is about 9.486833, or exactly 3√10. It lies between 9 and 10.

As a decimal
≈ 9.486833
Simplified surd
√90 = 3√10
Between
9 < √90 < 10
Squared
90² = 8100
Cube root
∛90 ≈ 4.481405

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.

√90 = √(9 × 10) = 3√10

Nearby numbers

√87 = √87√88 = 2√22√89 = √89√91 = √91√92 = 2√23√93 = √93

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 90?

About 9.486833, or exactly 3√10.

Q. Can the surd be simplified?

Yes: 90 = 9 × 10, so 3 comes out and it becomes 3√10.

Q. Between which integers does it fall?

Between 9 and 10.

Q. What is the cube root of 90?

About 4.481405.