Question

evaluate 3√9261/8000​

Answer 1

Answer:

21/20 is the answer.

Step-by-step explanation:

9261 is the cube of 21 and 8000 is the cube of 20.

Answer 2

Answer:

Required answer is $1\frac{1}{20}$

Step-by-step explanation:

Given,

$\sqrt[3]{ \frac{9261}{8000} }$

By prime factorisation,

$9261 = 3 \times 3 \times 3 \times 7 \times 7 \times 7 \\ 8000 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 5 \times 5 \times 5$

We can write,

$9261 = {(3 \times 7)}^{3} \\ = {21}^{3} \\ and \: 8000 = {(2 \times 5 \times 2)}^{3} \\ = {20}^{3}$

So,

$\sqrt[3]{ \frac{9261}{8000} } = { (\frac{9261}{8000} )}^{ \frac{1}{3} } \\ = (\frac{ {21}^{3} }{ {20}^{3} } ) ^{ \frac{1}{3} } \\ = \frac{ {21}^{3 \times \frac{1}{3} } }{ {20}^{3 \times \frac{1}{3} } } \\ = \frac{21}{20} \\ = 1 \frac{1}{20}$

Here applied formula is

${x}^{ {a}^{b} } = {x}^{a \times b} \\ \sqrt[x]{y} = {y}^{ \frac{1}{x} }$

This is a problem of Power of indices.

Power of indices related some important formulas,

${x}^{0} = 1 \\ {x}^{1} = x \\ {x}^{a} \times {x}^{b} = {x}^{a + b} \\ \frac{ {x}^{a} }{ {x}^{b} } = {x}^{a - b} \\ {x}^{ {y}^{a} } = {x}^{ya} \\ {x}^{ - 1} = \frac{1}{x} \\ {x}^{a} \times {y}^{a} = {(xy)}^{a}$

Power of indices related two more questions:

https://brainly.in/question/20611233

https://brainly.in/question/8929724

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