Square roots·120
120 =
2√30
≈ 10.954451

Square root of 120 — 10.954451 (2√30)

Irrational

The square root of 120 is about 10.954451, or exactly 2√30. It lies between 10 and 11.

As a decimal
≈ 10.954451
Simplified surd
√120 = 2√30
Between
10 < √120 < 11
Squared
120² = 14400
Cube root
∛120 ≈ 4.932424

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.

120 = √(4 × 30) = 2√30

Nearby numbers

From 1 to 200

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 120?

About 10.954451, or exactly 2√30.

Q. Can the surd be simplified?

Yes: 120 = 4 × 30, so 2 comes out and it becomes 2√30.

Q. Between which integers does it fall?

Between 10 and 11.

Q. What is the cube root of 120?

About 4.932424.