Question

Find the smallest number by which 7776 is to be divided to get a perfect square?

Answer 1

SOLUTION

TO DETERMINE

The smallest number by which 7776 is to be divided to get a perfect square

EVALUATION

Here the given number is 7776

$\sf{ 7776 }$

$\sf{ = 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 3 \times 3\: }$

$\sf{ = {2}^{5} \times {3}^{5} \: }$

$\sf{ = {2}^{4} \times 2 \times {3}^{4} \times 3 \: }$

$\sf{ = {(2 \times 3)}^{4} \times 6 \: }$

$= \sf{ {6}^{4} \times 6 \: }$

$= \sf{ {( {6}^{2}) }^{2} \times 6 \: }$

$= \sf{ {36}^{2} \times 6 \: }$

$\sf{ \therefore \: \: 7776 = {(36)}^{2} \times 6 }$

So we have to divide 7776 by 6 in order to get a perfect square number

FINAL ANSWER

6 is the smallest number by which 7776 is to be divided to get a perfect square

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Answer 2

Step-by-step explanation:

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