$\frac{\sqrt{72} \div 2}{2}$
Answer (2)
Simplify the square root: 72 = 6 2 .
Divide the simplified square root by 2: 6 2 ÷ 2 = 3 2 .
Divide the result by 2 again: 2 3 2 .
The final simplified expression is 2 3 2 .
Explanation
Understanding the Expression We are asked to simplify the expression 2 72 ÷ 2 . Let's break it down step by step.
Simplifying the Square Root First, we simplify the square root. We know that 72 = 36 × 2 , so 72 = 36 × 2 = 36 × 2 = 6 2 .
Substituting Back Now we substitute this back into the original expression: 2 6 2 ÷ 2 .
Dividing the Numerator Next, we perform the division in the numerator: 6 2 ÷ 2 = 3 2 . So the expression becomes 2 3 2 .
Final Simplified Form The simplified expression is 2 3 2 . We can approximate the value of this expression as follows: 2 3 2 ≈ 2 3 × 1.414 ≈ 2 4.242 ≈ 2.121 .
Examples
Understanding how to simplify radical expressions is useful in many areas of mathematics, such as geometry and calculus. For example, when finding the length of the diagonal of a square with side length 3, you would use the Pythagorean theorem, which gives a diagonal length of 3 2 + 3 2 = 18 = 3 2 . Simplifying radical expressions allows for easier calculations and a better understanding of the relationships between different quantities.
To simplify 2 72 ÷ 2 , we first simplify 72 to get 6 2 , then divide this by 2 to obtain 3 2 , and finally divide by 2 again, resulting in 2 3 2 .
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