$\sqrt{\frac{12}{16}}$
Answer (2)
Simplify the fraction inside the square root: 16 12 = 4 3 .
Take the square root of the numerator and the denominator separately: 4 3 = 4 3 .
Simplify the expression: 4 3 = 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 = 2 3 Since 3 is a prime number, 3 cannot be simplified further. The square root of 4 is 2.
Final Answer Therefore, the simplified expression is 2 3 .
Examples
Imagine you are building a square garden and need to calculate the length of its diagonal. If the area of the garden is such that the side length can be expressed as 16 12 , then simplifying this expression helps you find the exact ratio involving 3 in relation to the diagonal's length. This kind of simplification is useful in various geometric and construction problems.
The expression 16 12 simplifies to 2 3 . First, the fraction is simplified to 4 3 , and then we take the square roots of the numerator and denominator separately. The final answer is 2 3 .
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