Simplify Two Square Roots Calculator

This calculator helps you simplify expressions like √a + √b or √a - √b using the difference of squares formula. It's particularly useful in algebra, calculus, and physics problems where square roots need to be combined.

How to Use This Calculator

To simplify two square roots:

Enter the value for a in the first input field
Enter the value for b in the second input field
Select whether you want to add or subtract the square roots
Click the "Calculate" button
View the simplified result and the step-by-step solution

The calculator will show you the simplified form of the expression and demonstrate how it was derived using the difference of squares formula.

The Formula Explained

The key formula used here is the difference of squares:

(√a ± √b)² = a + b ± 2√(ab)

This formula allows us to combine two square roots into a single square root expression. The calculator uses this formula in reverse to simplify expressions like √a + √b or √a - √b.

When you have an expression like √a + √b, you can square it to get a + b + 2√(ab). Then you can rearrange this to find the simplified form.

Worked Examples

Example 1: Simplifying √18 + √8

Let's simplify √18 + √8 using our calculator:

Enter a = 18
Enter b = 8
Select the addition operation
Click Calculate

The calculator will show the simplified form as 3√2 + 2√2 = 5√2.

Example 2: Simplifying √50 - √2

For √50 - √2:

Enter a = 50
Enter b = 2
Select the subtraction operation
Click Calculate

The calculator will show the simplified form as 5√2 - √2 = 4√2.

FAQ

What is the difference of squares formula?: The difference of squares formula is (√a ± √b)² = a + b ± 2√(ab). This formula is used to combine or simplify expressions with square roots.
When should I use this calculator?: Use this calculator when you need to simplify expressions like √a + √b or √a - √b. It's particularly useful in algebra problems, physics equations, and calculus.
Can I simplify expressions with more than two square roots?: This calculator is designed for expressions with exactly two square roots. For more complex expressions, you may need to use additional algebraic techniques.
What if the numbers under the square roots aren't perfect squares?: The calculator will still work, but the simplified form may not be as neat. It will still simplify the expression as much as possible.
Is there a way to verify the calculator's results?: Yes, you can verify the results by squaring the simplified expression and checking if it matches the original expression squared.