Square roots·√225
√225 =
15
Exact

Square root of 225 — 15

Exact

The square root of 225 is 15, because 15 × 15 = 225.

As a decimal
15
Simplified surd
√225 = 15
Between
15
Squared
225² = 50625
Cube root
∛225 ≈ 6.082202

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.

√225 = √(225 × 1) = 15

Nearby numbers

√222 = √222√223 = √223√224 = 4√14√226 = √226√227 = √227√228 = 2√57

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 225?

15 exactly.

Q. Can the surd be simplified?

Yes: 225 = 225 × 1, so 15 comes out and it becomes 15.

Q. Between which integers does it fall?

It is the whole number 15.

Q. What is the cube root of 225?

About 6.082202.