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Square Root of 169 Calculator

Reviewed by Calculator Editorial Team

Finding the square root of a number is a fundamental mathematical operation with practical applications in geometry, algebra, and many other fields. This guide explains how to calculate square roots, including the square root of 169, with clear examples and a dedicated calculator.

What is a square root?

The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3 because 3 × 3 = 9. Square roots are denoted by the radical symbol √, so √9 = 3.

Not all numbers have real square roots. For example, the square root of -1 is an imaginary number (i), while the square root of 0 is 0. In this guide, we'll focus on real, non-negative square roots.

How to calculate square roots

There are several methods to find square roots:

  1. Prime factorization: Break down the number into prime factors and pair them to find the square root.
  2. Long division method: A step-by-step algorithm for finding square roots of non-perfect squares.
  3. Using a calculator: The quickest method for most practical purposes.

For perfect squares (numbers that are squares of integers), the prime factorization method is often the simplest. For example, to find √169:

  1. Factorize 169: 169 = 13 × 13
  2. Pair the factors: (13 × 13)
  3. Take one from each pair: √169 = 13

Square root formula

Square Root Formula

The square root of a number x is written as √x and satisfies the equation:

√x = y where y × y = x

For the specific case of 169:

Square Root of 169

√169 = 13 because 13 × 13 = 169

Worked examples

Example 1: Finding √169

Using the prime factorization method:

  1. Factorize 169: 169 = 13 × 13
  2. Pair the factors: (13 × 13)
  3. Take one from each pair: √169 = 13

Verification: 13 × 13 = 169, so the calculation is correct.

Example 2: Finding √144

Using the prime factorization method:

  1. Factorize 144: 144 = 12 × 12 = (2 × 2 × 3) × (2 × 2 × 3)
  2. Pair the factors: (2 × 2 × 3) × (2 × 2 × 3)
  3. Take one from each pair: √144 = 12

Verification: 12 × 12 = 144, so the calculation is correct.

FAQ

What is the square root of 169?

The square root of 169 is 13, because 13 multiplied by itself equals 169.

How do I calculate square roots?

You can calculate square roots using prime factorization, the long division method, or by using a calculator. Our calculator provides the quickest method for most practical purposes.

What is the difference between a square and a square root?

A square of a number is the result of multiplying the number by itself (e.g., 5 squared is 25). A square root is a number that, when multiplied by itself, gives the original number (e.g., the square root of 25 is 5).

Can all numbers have square roots?

No, only non-negative real numbers have real square roots. Negative numbers have imaginary square roots, and numbers like 2 do not have perfect square roots (they have irrational square roots).