Cal11 calculator
Search calculator...

Simplify Sq Root Calculator

Reviewed by Calculator Editorial Team

Simplifying square roots is a fundamental math skill that helps in algebra, calculus, and many other areas of mathematics. This calculator makes it easy to simplify any square root expression into its simplest radical form.

How to Use This Calculator

Using our simplify square root calculator is straightforward:

  1. Enter the radicand (the number under the square root) in the input field.
  2. Click the "Calculate" button to simplify the square root.
  3. View the simplified result and see the step-by-step simplification process.
  4. Use the "Reset" button to clear the calculator for a new calculation.

The calculator will show you the simplified form of the square root and explain how it was achieved.

How Square Root Simplification Works

Simplifying a square root involves factoring the radicand into perfect squares and square roots. The general formula for simplifying √a is:

√a = √(b² × c) = b × √c

Where b² is the largest perfect square that divides a, and c is the remaining factor.

Here's how the simplification process works:

  1. Factor the radicand into perfect squares and other factors.
  2. Separate the square roots of the perfect squares from the other factors.
  3. Multiply the square roots of the perfect squares together.
  4. Combine the results to get the simplified radical form.

Note: The radicand must be a positive integer for this calculator to work. Negative numbers and non-integers will not produce valid results.

Examples of Simplified Square Roots

Let's look at some examples to see how square roots are simplified:

Example 1: Simplifying √36

36 is a perfect square (6²), so:

√36 = √(6²) = 6 × √1 = 6

Example 2: Simplifying √72

72 can be factored into 36 × 2, and 36 is a perfect square:

√72 = √(36 × 2) = √36 × √2 = 6√2

Example 3: Simplifying √108

108 can be factored into 36 × 3, and 36 is a perfect square:

√108 = √(36 × 3) = √36 × √3 = 6√3

Example 4: Simplifying √200

200 can be factored into 100 × 2, and 100 is a perfect square:

√200 = √(100 × 2) = √100 × √2 = 10√2

Frequently Asked Questions

What is the simplest form of a square root?
The simplest form of a square root is when the radicand has no perfect square factors other than 1. This means the square root cannot be simplified further.
Can I simplify square roots of negative numbers?
No, this calculator only works with positive integers. Negative numbers and non-integers cannot be simplified using this tool.
What if the radicand is not a perfect square?
If the radicand is not a perfect square, the calculator will simplify it as much as possible by factoring out the largest perfect square factor.
How do I simplify nested square roots?
Nested square roots can be simplified by multiplying the radicands and then simplifying the resulting square root as you would normally.