Question

find the cube root of 19683 by prime factorization method full solution

Answer 1

3|19683
3|6561
3|2187
3|729
3|243
3|81
3|27
3|9
3|3
19683 = {3×3×3}×{3×3×3}×{3×3×3}
19683 = 27×27×27
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Answer 2

$\large{\boxed{\boxed{\boxed{\bold{\green{Solution :\longrightarrow}}}}}}$

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

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

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

$\bold{Have \: \: a \: \: nice \: \: day.}$