Square Root Calculator for Radicals

This square root calculator helps you find square roots of numbers and simplify radicals. Whether you're solving math problems, working with geometry, or analyzing data, this tool provides accurate results and clear explanations.

How to Use This Calculator

Using our square root calculator is simple:

Enter the number you want to find the square root of in the input field.
Select whether you want the exact radical form or a decimal approximation.
Click the "Calculate" button to get the result.
Review the detailed explanation and example calculations.

The calculator will display the square root in both radical form (√) and decimal form, along with a step-by-step explanation of how the calculation was performed.

Formula Explained

The square root of a number x is a value that, when multiplied by itself, gives x. Mathematically, this is represented as:

Square Root Formula

√x = y, where y × y = x

For example, the square root of 25 is 5 because 5 × 5 = 25. The calculator uses this fundamental relationship to find square roots.

Worked Examples

Let's look at a couple of examples to see how the square root calculator works in practice.

Example 1: Simple Square Root

Find the square root of 36.

Calculation Steps

1. We know that 6 × 6 = 36.

2. Therefore, √36 = 6.

Result: √36 = 6

Example 2: Radical Form

Find the square root of 50 in radical form.

Calculation Steps

1. Factor 50 into 25 × 2.

2. √(25 × 2) = √25 × √2 = 5√2.

Result: √50 = 5√2

Simplifying Radicals

Simplifying radicals involves expressing a square root in its simplest radical form. This is done by factoring the number under the square root into a product of perfect squares and other factors.

Simplifying Radicals Formula

√(a × b) = √a × √b

For example, to simplify √72:

Factor 72 into 36 × 2.
√(36 × 2) = √36 × √2 = 6√2.

The simplified form is 6√2, which is easier to work with in mathematical expressions.

Frequently Asked Questions

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

The square root of a number is the value that, when multiplied by itself, gives the original number. A radical is the symbol (√) used to represent a square root. For example, √9 is the radical form of the square root of 9, which equals 3.

Can I find the square root of a negative number?

In real numbers, the square root of a negative number is not defined. However, in complex numbers, negative numbers have square roots. This calculator works with real numbers only.

How do I simplify a radical expression?

To simplify a radical expression, factor the number under the square root into a product of perfect squares and other factors. Then, take the square root of the perfect square and leave the other factors under the radical. For example, √50 simplifies to 5√2.