How do you simplify the square root of 175 minus the square root of 28?

To simplify the expression, we calculate and simplify each square root term individually and then combine the results.

Expression: √175 - √28

Step 1: Simplify √175
Prime factorization of 175:
175 = 25 × 7 = (5 × 5) × 7
Write √175 using the factors:
√175 = √(25 × 7) = √25 × √7 = 5√7
Thus, √175 simplifies to 5√7.

Step 2: Simplify √28
Prime factorization of 28:
28 = 4 × 7 = (2 × 2) × 7
Write √28 using the factors:
√28 = √(4 × 7) = √4 × √7 = 2√7
Thus, √28 simplifies to 2√7.

Step 3: Combine the results
Substituting the simplified forms into the original expression:
√175 - √28 = 5√7 - 2√7
Combine like terms:
5√7 - 2√7 = (5 - 2)√7 = 3√7
Final Answer:
The simplified form of the expression √175 - √28 is 3√7.