\frac{\sqrt{13}}{2}+\frac{2 \sqrt{13}}{3}
Answer (2)
The expression 2 13 + 3 2 13 simplifies to 6 7 13 by factoring out 13 and finding a common denominator for the fractions. After adding the fractions, we multiply by 13 to get the final simplified result.
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Factor out the common factor 13 : 13 ( 2 1 + 3 2 ) .
Find a common denominator and add the fractions: 2 1 + 3 2 = 6 3 + 6 4 = 6 7 .
Multiply the result by 13 : 6 7 13 .
The simplified expression is 6 7 13 .
Explanation
Understanding the Expression We are given the expression 2 13 + 3 2 13 . Our goal is to simplify this expression by combining the two terms.
Factoring out the Common Factor First, we can factor out the common factor of 13 from both terms: 2 13 + 3 2 13 = 13 ( 2 1 + 3 2 )
Finding a Common Denominator Now, we need to add the fractions 2 1 and 3 2 . To do this, we find a common denominator, which is 6. We rewrite the fractions with the common denominator: 2 1 = 6 3 and 3 2 = 6 4
Adding the Fractions Now we can add the fractions: 6 3 + 6 4 = 6 3 + 4 = 6 7
Multiplying by the Square Root Finally, we multiply the result by 13 : 13 × 6 7 = 6 7 13 So, the simplified expression is 6 7 13 .
Examples
Understanding how to simplify expressions with radicals is useful in various fields, such as physics and engineering, where you often encounter expressions involving square roots when calculating distances, areas, or volumes. For example, when dealing with the Pythagorean theorem ( a 2 + b 2 = c 2 ), you might need to simplify expressions like the one in this problem to find the length of a side of a right triangle. Simplifying such expressions makes further calculations easier and more accurate.
