Comparison of Square Roots

1. Comparison of Square Roots
   For and :
1. If , then
2. If , then
3. If , then


2. Understanding the Comparison of Square Roots Using the Area of a Square
1. The larger the area of a square, the longer its side length.
   If , then
2. The longer the side length of a square, the larger its area.
   If , then

3. Comparing and (where and )
• •Method 1: Express the number without the square root as a square root and compare
  Compare and
• •Method 2: Square both sides and compare
  Compare and


4. Inequalities Involving Square Roots
   For and , to solve the inequality ,
   square both sides: