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Simplify The Following Radical Expression Calculator

Reviewed by Calculator Editorial Team

Simplifying radical expressions is a fundamental algebra skill that helps you work with square roots and other roots more efficiently. This calculator will help you simplify expressions like √(a²b) or √(18) to their simplest form.

How to Use This Calculator

To simplify a radical expression using our calculator:

  1. Enter the radicand (the number inside the square root) in the input field
  2. Click the "Calculate" button
  3. Review the simplified result and step-by-step explanation

The calculator will show you the simplified form and explain each step of the simplification process.

Radical Simplification Rules

To simplify a square root (or any radical), follow these steps:

  1. Factor the radicand into perfect squares and other factors
  2. Separate the square root into factors
  3. Take the square root of the perfect squares
  4. Combine the results

Simplification Formula

√(a·b) = √a · √b

√(a²·b) = a·√b

For example, √(72) can be simplified by factoring 72 into 36 × 2, then taking the square root of 36 (which is 6) and leaving the square root of 2.

Worked Examples

Example 1: Simplifying √(72)

  1. Factor 72: 72 = 36 × 2
  2. √(72) = √(36 × 2) = √36 × √2 = 6√2

Example 2: Simplifying √(50)

  1. Factor 50: 50 = 25 × 2
  2. √(50) = √(25 × 2) = √25 × √2 = 5√2

Remember that only perfect squares can be taken out of the radical. For example, √(18) cannot be simplified further because 18 doesn't have any perfect square factors other than 1.

Frequently Asked Questions

What is a radical expression?
A radical expression is any expression that contains a square root (√), cube root (∛), or other root symbol. Examples include √(16) and ∛(27).
How do I simplify a radical expression?
To simplify a radical expression, factor the radicand into perfect squares and other factors, then separate the square root into factors, taking the square root of the perfect squares.
Can I simplify √(18) further?
No, √(18) cannot be simplified further because 18 doesn't have any perfect square factors other than 1. The simplified form is √(18).
What if the radicand is negative?
If the radicand is negative, the expression is not a real number. For example, √(-1) is not a real number. You would need to use imaginary numbers to represent this.