Square Roots in Radical Form Calculator

This calculator helps you find square roots in radical form. Whether you're solving math problems or working with real-world measurements, understanding square roots in radical notation is essential. The calculator provides exact square roots when possible and simplifies them to their simplest radical form.

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 roots of 9 are 3 and -3 because 3 × 3 = 9 and (-3) × (-3) = 9.

Square roots are fundamental in mathematics, physics, engineering, and many other fields. They appear in calculations involving areas, distances, and other geometric measurements.

Square roots in radical notation

Square roots are commonly expressed using radical notation, which uses the symbol √ (the radical symbol). For example, the square root of 25 is written as √25, which equals 5.

When a square root cannot be simplified to a whole number, it's expressed in radical form. For example, √8 simplifies to 2√2 because 8 = 4 × 2 and √4 = 2.

Square Root Formula

√a = b, where b × b = a

How to calculate square roots

Step 1: Identify the number

First, determine the number for which you want to find the square root. This can be any positive real number.

Step 2: Check for perfect squares

If the number is a perfect square (like 16, 25, 36), its square root will be a whole number. For example, √16 = 4.

Step 3: Simplify non-perfect squares

For numbers that aren't perfect squares, simplify the square root by factoring out perfect squares. For example, √50 = √(25 × 2) = √25 × √2 = 5√2.

Step 4: Use the calculator

For complex numbers or when simplification isn't straightforward, use the square root calculator to get the exact radical form.

Examples of square roots

Example 1: Perfect Square

Find √36.

Solution: √36 = 6 because 6 × 6 = 36.

Example 2: Non-Perfect Square

Find √50.

Solution: √50 = 5√2 because 50 = 25 × 2 and √25 = 5.

Example 3: Complex Number

Find √(-9).

Solution: √(-9) = 3i, where i is the imaginary unit (i² = -1).

FAQ

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

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

Can square roots be negative?

Yes, square roots can be negative. For example, √9 = 3 and -3 because both 3 × 3 and (-3) × (-3) equal 9.

How do I simplify square roots?

To simplify √a, factor a into a product of perfect squares and other factors. For example, √18 = √(9 × 2) = 3√2.