Let's simplify the expression \( \frac{405 \sqrt{63}}{\sqrt{1}} \).
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Simplifying \( \sqrt{63} \): \[ \sqrt{63} = \sqrt{9 \cdot 7} = \sqrt{9} \cdot \sqrt{7} = 3\sqrt{7} \]
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Substituting back: Now, substitute \( \sqrt{63} \) into the original expression: \[ 405 \sqrt{63} = 405 \cdot 3\sqrt{7} = 1215\sqrt{7} \]
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Finding the quotient: Since the denominator is \( \sqrt{1} = 1 \), the expression simplifies to: \[ \frac{1215\sqrt{7}}{1} = 1215\sqrt{7} \]
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Simplifying 1215: We can also factor 1215: \[ 1215 = 3^5 \times 5 \text{ (since } 1215 = 27 \times 45 = 27 \times 9 \times 5 = 3^3 \times (3^2 \times 5) \text{)} \]
This simplifies to: \[ 1215 = 15 \cdot 81 = 15 \cdot 9 \cdot 3 \] In simplest radical terms, \[ \frac{1215 \sqrt{7}}{1} \]
Thus, the answer should therefore simplify or present as needed.
Now, looking through the response choices provided, it seems none match exactly.
However:
- From the options provided, it seems that the best comparison with \( 1215\sqrt{7} \) might be \( 35\sqrt{15} \) but does not match with what we calculated.
Since there may be an oversight with respecting the available choices to select from, let's provide the key correct simplification:
- It appears we should have \( 1215\sqrt{7} \) as a rational quotient with radical simplified.
I might miss parsing your problem statement accurately on logical framing of quotient or presentation.
Would you want me to elaborate further with another specific breakdown?