Question

method to find cube root of 19683​

Answer 1

Answer:

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3 | 19683

3 | 6561

3 | 2187

3 | 729

3 | 243

3 | 81

3 | 27

3 | 9

3 | 3

..... 1

Resolving 19683 into prime factors , we get

\bold{19683 = 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{= {3}^{3} \times {3}^{3} \times {3}^{3} }

\bold{ \sqrt[3]{19683} = \sqrt[3]{3 {}^{3} \times {3}^{3} \times {3}^{3} }} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\bold{= 3 \times 3 \times 3} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{= 27}❤️❤️

Step-by-step explanation:

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Answer 2

Answer:

(27)^3

Step-by-step explanation:

19683 = 3*6561

= 3*3*2187

= 9*3*729

= 9*3*27*27

= 9*9*9*3*3*3

= (9*3)^3

So, 27^3 = 19683