Question

the least natural number multiplied with 2 power 7 × 3 power 6 to make it as a perfect cube is
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Answer 1

Answer:

2

Step-by-step explanation:

$\sqrt{ {2}^{7} \times {3}^{6} } \\ = \sqrt{ {2}^{6} \times 2 \times {3}^{6} } \\ = {2}^{3} \times {3}^{3} \sqrt{2}$

So, 2 should be multiplied to it to make a perfect square.

Answer 2

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$given \: no. = ({2}^{7} \times {3}^{6} )$

since we can see that if this will be under a cube root then, (3^6) will come out as +ve integer but (2^7) willn't.

Hence , we have to multiply (2^2) for getting a +ve integer out of cube root.

Now the no. will be :-

$( {2}^{9} \times {3}^{6} )$

now,

$\sqrt[3]{ {2}^{9} \times {3}^{6} }$

$= \sqrt[3]{2.2.2.2.2.2.2.2.2 \times 3.3.3.3.3.3}$

$= {2}^{3} \times {3}^{2}$

$= 8 \times 9$

= 72

HOPE IT WILL HELP YOU..

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