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Subtract and Simplify Square Roots Calculator

Reviewed by Calculator Editorial Team

This calculator helps you subtract and simplify square roots by following mathematical rules. Whether you're studying algebra or need to solve a problem, this tool provides step-by-step guidance and accurate results.

How to Use This Calculator

Using the subtract and simplify square roots calculator is straightforward. Follow these steps:

  1. Enter the first square root in the first input field. For example, √8.
  2. Enter the second square root in the second input field. For example, √2.
  3. Click the "Calculate" button to see the result.
  4. Review the simplified form of the subtraction.

The calculator will display the simplified form of the subtraction, such as √8 - √2 = √6.

How It Works

Subtracting and simplifying square roots involves several mathematical steps. Here's how the calculator performs the calculation:

  1. Identify the radicands (the numbers inside the square roots).
  2. Check if the radicands are perfect squares or can be simplified.
  3. Subtract the square roots if they have the same radicand.
  4. Simplify the result if possible.

Formula Used

√a - √b = √(a - b) if a ≥ b and both a and b are non-negative.

Assumptions

The calculator assumes that the radicands are non-negative and that the first radicand is greater than or equal to the second.

Worked Examples

Let's look at a couple of examples to understand how the calculator works.

Example 1: √18 - √8

Step 1: Identify the radicands: 18 and 8.

Step 2: Check if the radicands can be simplified. √18 = 3√2 and √8 = 2√2.

Step 3: Subtract the simplified forms: 3√2 - 2√2 = √2.

Final result: √18 - √8 = √2.

Example 2: √27 - √9

Step 1: Identify the radicands: 27 and 9.

Step 2: Simplify the square roots: √27 = 3√3 and √9 = 3.

Step 3: Subtract the simplified forms: 3√3 - 3 = 3(√3 - 1).

Final result: √27 - √9 = 3(√3 - 1).

Frequently Asked Questions

Can I subtract square roots with different radicands?
No, you can only subtract square roots if they have the same radicand. If the radicands are different, the calculator will not simplify the expression further.
What if the first radicand is smaller than the second?
The calculator will display a negative result if the first radicand is smaller than the second. For example, √4 - √9 = -√5.
Can I simplify square roots with variables?
This calculator is designed for numerical square roots. For algebraic expressions, you may need a more advanced tool.