Square roots·√169
√169 =
13
Exact

Square root of 169 — 13

Exact

The square root of 169 is 13, because 13 × 13 = 169.

As a decimal
13
Simplified surd
√169 = 13
Between
13
Squared
169² = 28561
Cube root
∛169 ≈ 5.528775

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.

√169 = √(169 × 1) = 13

Nearby numbers

√166 = √166√167 = √167√168 = 2√42√170 = √170√171 = 3√19√172 = 2√43

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 169?

13 exactly.

Q. Can the surd be simplified?

Yes: 169 = 169 × 1, so 13 comes out and it becomes 13.

Q. Between which integers does it fall?

It is the whole number 13.

Q. What is the cube root of 169?

About 5.528775.