\sqrt{\frac{12}{16}}
Answer (1)
Simplify the fraction inside the square root: 16 12 = 4 3 .
Take the square root of the numerator and denominator separately: 4 3 = 4 3 .
Simplify the square root of the denominator: 2 3 .
The simplified expression is 2 3 .
Explanation
Understanding the Problem We are given the expression 16 12 and our goal is to simplify it.
Simplifying the Fraction First, we simplify the fraction inside the square root. We can divide both the numerator and the denominator by their greatest common divisor, which is 4. So, we have 16 12 = 16 ÷ 4 12 ÷ 4 = 4 3 Now our expression becomes 4 3 .
Taking Square Roots Next, we take the square root of the numerator and the square root of the denominator separately: 4 3 = 4 3 Since 4 = 2 , we have 2 3 The square root of 3 cannot be simplified further, so our final simplified expression is 2 3 .
Final Answer Therefore, the simplified form of 16 12 is 2 3 .
Examples
Imagine you are calculating the length of the diagonal of a rectangle. If the sides of the rectangle are related in such a way that the ratio of some intermediate calculation simplifies to 16 12 , then simplifying this expression to 2 3 helps you find the exact length more easily. This kind of simplification is useful in various geometric and algebraic problems where exact values are needed.
