Question

Find the smallest number by which 83349 must be divided so that the quotient is a perfect cube. Also find the cube root of the quotient.

Answer 1

$Resolving \: 83349 \: into \:prime \:factors ,\\we \:get$

3 | 83349

__________

3 | 27783

__________

3 | 9261

__________

3 | 3987

__________

3 | 1029

__________

7 | 343

__________

7 | 49

__________

***** 7

83349 = 3 × 3 × 3 × 3 × 3 × 7 × 7 × 7

The prime factor 3 doesn't appear in a group of

three factors .

So, 83349 is not a perfect cube.

Hence, the smallest number which is to be divided to make it a perfect cube is 3 × 3= 9.

$\red{ Required \: perfect \:cube } \\= \frac{83349}{9} \\= \frac{3^{5} \times 7^{3}}{3^{2}} \\= 3^{3} \times 7^{3} \\= ( 3 \times 7 )^{3} \\= (21)^{3}$

♪••.

Answer 2

Answer:

it is 9

Step-by-step explanation: