To simplify square roots, you can follow these steps:
1. **Factorize the Number Inside the Square Root**: Write the number inside the square root as the product of its factors.
2. **Identify Perfect Square Factors**: Look for perfect square factors among the factors obtained in step 1. A perfect square is a number that is the square of an integer (1, 4, 9, 16, 25, etc.).
3. **Take Out Perfect Square Factors**: Take the square root of the perfect square factors identified in step 2 and move them outside the square root. Write the remaining factors inside the square root.
4. **Multiply and Combine**: Multiply any factors left inside the square root and simplify the expression if possible.
Here's an example to illustrate the process:
Let's simplify √48:
1. Factorize 48: 48 = 2 × 2 × 2 × 2 × 3.
2. Identify perfect square factors: 4 (2 × 2) is a perfect square.
3. Take out the perfect square factor: √48 = √(4 × 12) = √4 × √12.
4. Simplify: √4 = 2, so √48 = 2√12.
So, √48 simplifies to 2√12.
Another example:
Let's simplify √75:
1. Factorize 75: 75 = 3 × 5 × 5.
2. Identify perfect square factors: There are no perfect square factors.
3. Take out the perfect square factor: There are no perfect square factors to take out.
4. Simplify: √75 remains as √75.
So, √75 cannot be further simplified as there are no perfect square factors. It is left in its simplified form.
By following these steps, you can simplify square roots to their simplest form. Practice with various numbers to become more comfortable with the process.