Simplify the expression (15√3)/(√5)
Understand the Problem
The question is asking how to simplify the expression involving square roots: ( \frac{15\sqrt{3}}{\sqrt{5}} ). We will simplify this expression step by step.
Answer
The simplified expression is \( 3\sqrt{15} \).
Answer for screen readers
The simplified expression is ( 3\sqrt{15} ).
Steps to Solve
- Simplifying the Fraction
To simplify ( \frac{15\sqrt{3}}{\sqrt{5}} ), we recognize that we can multiply both the numerator and the denominator by ( \sqrt{5} ) to eliminate the square root in the denominator.
[ \frac{15\sqrt{3}}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}} = \frac{15\sqrt{3} \cdot \sqrt{5}}{5} ]
- Combining the Square Roots
Next, we can combine the square roots in the numerator.
[ \sqrt{3} \cdot \sqrt{5} = \sqrt{15} ]
So the fraction becomes:
[ \frac{15\sqrt{15}}{5} ]
- Simplifying the Final Fraction
Now, we can simplify ( \frac{15\sqrt{15}}{5} ) by dividing ( 15 ) by ( 5 ):
[ 3\sqrt{15} ]
The simplified expression is ( 3\sqrt{15} ).
More Information
This simplification method utilizes the property of square roots that states ( \sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b} ).
Tips
- Neglecting to Rationalize the Denominator: Always ensure to eliminate any square roots from denominators for a more simplified expression.
- Not Combining Square Roots: Forgetting that ( \sqrt{a} \cdot \sqrt{b} = \sqrt{ab} ) can lead to errors in the calculations.
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