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Simplify Square Root Addition Calculator

Reviewed by Calculator Editorial Team

Adding square roots can be simplified using specific algebraic rules. This calculator helps you add square roots step by step, with clear examples and formulas to understand the process.

How to Use This Calculator

To use the simplify square root addition calculator:

  1. Enter the coefficients for the first square root in the first input field.
  2. Enter the radicand (number inside the square root) for the first square root in the second input field.
  3. Enter the coefficients for the second square root in the third input field.
  4. Enter the radicand for the second square root in the fourth input field.
  5. Click the "Calculate" button to see the simplified result.
  6. Use the "Reset" button to clear all fields and start over.

The calculator will show you the simplified form of the square root addition, including any common factors that can be extracted.

Formula Explained

When adding two square roots with the same radicand, you can combine them using the following formula:

√a + √a = 2√a

For different radicands, the square roots cannot be combined directly.

For example, √4 + √4 simplifies to 2√4, which further simplifies to 4.

If the radicands are different, like √2 + √3, they cannot be combined further.

Worked Examples

Example 1: Same Radicands

Calculate √9 + √9:

  1. Identify the radicands: both are 9.
  2. Apply the formula: √9 + √9 = 2√9.
  3. Simplify √9 to 3.
  4. Final result: 2 × 3 = 6.

Example 2: Different Radicands

Calculate √5 + √7:

  1. Identify the radicands: 5 and 7.
  2. Since the radicands are different, the expression cannot be simplified further.
  3. Final result: √5 + √7.

FAQ

Can I add square roots with different radicands?
No, square roots with different radicands cannot be combined directly. They must remain as separate terms.
What happens if the radicands are the same?
The coefficients can be combined, and the radicand remains the same. For example, √a + √a = 2√a.
Can I simplify √a + √b further?
No, unless a and b have a common factor that can be extracted. For example, √8 + √2 = √(4×2) + √2 = 2√2 + √2 = 3√2.