How to Simplify Square Root on Calculator

Introduction

A square root of a number is a value that, when multiplied by itself, gives the original number. For example, √9 = 3 because 3 × 3 = 9. However, not all square roots are simple integers. Some square roots, like √8, are irrational numbers that cannot be expressed as simple fractions.

Simplifying square roots means expressing them in a form that makes calculations easier. This typically involves factoring the number under the square root into perfect squares and other factors.

Simplification Methods

Step 1: Factor the Number

The first step in simplifying a square root is to factor the number under the radical into perfect squares and other factors. A perfect square is a number that is the square of an integer (e.g., 1, 4, 9, 16, 25, etc.).

Step 2: Separate the Square Root

Next, separate the square root into two parts: one part containing the perfect square and the other part containing the remaining factors.

Step 3: Simplify the Perfect Square

Simplify the square root of the perfect square by taking the square root of the perfect square and multiplying it by the remaining square root.

Additional Tips

• Always look for the largest perfect square factor to simplify the square root as much as possible.
• If the number under the square root is a fraction, simplify the numerator and denominator separately.
• If the number under the square root is negative, the result will be an imaginary number (e.g., √(-1) = i).

Worked Examples

Example 1: Simplifying √48

Step 1: Factor 48 into perfect squares and other factors.

48 = 16 × 3 = 4² × 3

Step 2: Separate the square root.

√48 = √(16 × 3) = √16 × √3

Step 3: Simplify the perfect square.

√16 × √3 = 4 × √3 = 4√3

Example 2: Simplifying √50

Step 1: Factor 50 into perfect squares and other factors.

50 = 25 × 2 = 5² × 2

Step 2: Separate the square root.

√50 = √(25 × 2) = √25 × √2

Step 3: Simplify the perfect square.

√25 × √2 = 5 × √2 = 5√2

Example 3: Simplifying √(18/50)

Step 1: Simplify the fraction inside the square root.

18/50 = 9/25

Step 2: Separate the square root.

√(9/25) = √9 / √25

Step 3: Simplify the perfect squares.

√9 / √25 = 3 / 5 = 0.6

Calculator Tips

Using a Scientific Calculator

Most scientific calculators have a square root function (√). To simplify a square root on a calculator:

1. Enter the number you want to find the square root of.
2. Press the √ button.
3. The calculator will display the simplified square root.

Using a Graphing Calculator

Graphing calculators can also simplify square roots. Follow these steps:

1. Enter the number under the square root.
2. Use the square root function (√).
3. The calculator will display the simplified result.

Using Online Calculators

Online calculators can simplify square roots quickly. Simply enter the number, and the calculator will provide the simplified square root.