$\frac{2 \sqrt{2}}{\sqrt{6}}+\frac{1}{\sqrt{3}}$?
Answer (2)
The given expression 6 2 2 + 3 1 simplifies to 3 after combining fractions and rationalizing the denominator.
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Simplify the first term: 6 2 2 = 3 2 .
Add the two terms: 3 2 + 3 1 = 3 3 .
Rationalize the denominator: 3 3 = 3 3 3 .
Simplify to get the final answer: 3 .
Explanation
Understanding the Problem We are asked to simplify the expression 6 2 2 + 3 1 . This involves simplifying radicals and rationalizing denominators to arrive at a simplified expression.
Simplifying the First Term First, let's simplify the first term. We have 6 2 2 = 2 ⋅ 3 2 2 = 2 3 2 2 = 3 2 So the expression becomes 3 2 + 3 1
Adding the Fractions Now, we have a common denominator, so we can add the fractions: 3 2 + 3 1 = 3 2 + 1 = 3 3
Rationalizing the Denominator To rationalize the denominator, we multiply the numerator and denominator by 3 :
3 3 = 3 3 3 3 = 3 3 3 = 3 Thus, the simplified expression is 3 .
Final Answer Therefore, the simplified value of the expression 6 2 2 + 3 1 is 3 .
Examples
Imagine you are constructing a triangular garden bed and need to calculate the length of one of its sides. If the side length is represented by the expression 6 2 2 + 3 1 , simplifying this expression to 3 gives you the exact length you need for your construction. Understanding how to simplify radical expressions is crucial in various fields like engineering, physics, and architecture, where precise measurements are essential for design and construction.
