Square roots·√53
√53 =
√53
≈ 7.28011

Square root of 53 — 7.28011 (√53)

Irrational

The square root of 53 is about 7.28011, or exactly √53. It lies between 7 and 8.

As a decimal
≈ 7.28011
Simplified surd
√53 = √53
Between
7 < √53 < 8
Squared
53² = 2809
Cube root
∛53 ≈ 3.756286

Nearby numbers

√50 = 5√2√51 = √51√52 = 2√13√54 = 3√6√55 = √55√56 = 2√14

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 53?

About 7.28011, or exactly √53.

Q. Can the surd be simplified?

No — there is no square factor to pull out.

Q. Between which integers does it fall?

Between 7 and 8.

Q. What is the cube root of 53?

About 3.756286.