Square roots·√51
√51 =
√51
≈ 7.141428

Square root of 51 — 7.141428 (√51)

Irrational

The square root of 51 is about 7.141428, or exactly √51. It lies between 7 and 8.

As a decimal
≈ 7.141428
Simplified surd
√51 = √51
Between
7 < √51 < 8
Squared
51² = 2601
Cube root
∛51 ≈ 3.70843

Nearby numbers

√48 = 4√3√49 = 7√50 = 5√2√52 = 2√13√53 = √53√54 = 3√6

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 51?

About 7.141428, or exactly √51.

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 51?

About 3.70843.