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Answer :
Sure, let's simplify the expression [tex]\(\sqrt{\frac{63 x^{15}}{7 x}}\)[/tex] step by step.
1. Simplify Inside the Square Root:
- Start by simplifying the fraction inside the square root: [tex]\(\frac{63 x^{15}}{7 x}\)[/tex].
2. Divide the Coefficients:
- Divide the numbers: [tex]\(\frac{63}{7} = 9\)[/tex].
3. Simplify the Variables:
- For the variables, subtract the exponents: [tex]\(x^{15} / x^1 = x^{15-1} = x^{14}\)[/tex].
4. Write the Simplified Expression Inside the Square Root:
- Now the expression inside the square root is: [tex]\(9x^{14}\)[/tex].
5. Simplify the Square Root:
- Break down the square root: [tex]\(\sqrt{9x^{14}} = \sqrt{9} \times \sqrt{x^{14}}\)[/tex].
6. Compute Each Square Root:
- [tex]\(\sqrt{9} = 3\)[/tex].
- [tex]\(\sqrt{x^{14}} = x^{14/2} = x^7\)[/tex] because taking the square root is the same as raising to the power of [tex]\(\frac{1}{2}\)[/tex].
7. Combine the Results:
- Combine these results: [tex]\(3 \times x^7 = 3x^7\)[/tex].
Therefore, the simplified form of [tex]\(\sqrt{\frac{63 x^{15}}{7 x}}\)[/tex] is [tex]\(\boxed{3x^7}\)[/tex].
1. Simplify Inside the Square Root:
- Start by simplifying the fraction inside the square root: [tex]\(\frac{63 x^{15}}{7 x}\)[/tex].
2. Divide the Coefficients:
- Divide the numbers: [tex]\(\frac{63}{7} = 9\)[/tex].
3. Simplify the Variables:
- For the variables, subtract the exponents: [tex]\(x^{15} / x^1 = x^{15-1} = x^{14}\)[/tex].
4. Write the Simplified Expression Inside the Square Root:
- Now the expression inside the square root is: [tex]\(9x^{14}\)[/tex].
5. Simplify the Square Root:
- Break down the square root: [tex]\(\sqrt{9x^{14}} = \sqrt{9} \times \sqrt{x^{14}}\)[/tex].
6. Compute Each Square Root:
- [tex]\(\sqrt{9} = 3\)[/tex].
- [tex]\(\sqrt{x^{14}} = x^{14/2} = x^7\)[/tex] because taking the square root is the same as raising to the power of [tex]\(\frac{1}{2}\)[/tex].
7. Combine the Results:
- Combine these results: [tex]\(3 \times x^7 = 3x^7\)[/tex].
Therefore, the simplified form of [tex]\(\sqrt{\frac{63 x^{15}}{7 x}}\)[/tex] is [tex]\(\boxed{3x^7}\)[/tex].
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