Rewrite the division as a fraction.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Rewrite the division as a fraction.
$$ 4\sqrt{15} \div 2\sqrt{5} = \frac{4\sqrt{15}}{2\sqrt{5}} $$
Step 2: Simplify the numerical coefficients and the surds separately.
$$ \frac{4}{2} \times \frac{\sqrt{15}}{\sqrt{5}} $$
Step 3: Perform the division for the coefficients.
$$ 2 \times \frac{\sqrt{15}}{\sqrt{5}} $$
Step 4: Use the property $\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$ to simplify the surds.
$$ 2 \times \sqrt{\frac{15}{5}} $$
Step 5: Perform the division inside the square root.
$$ 2 \times \sqrt{3} $$
The simplified expression is:
$$ \boxed{2\sqrt{3}} $$
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