Question

What is the smallest number that should divide 3645 to get a perfect cube . Also find cube root
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Answer 1

$\huge\sf\pink{Answer}$

☞ We have to subtract the number by 5 & the cube root we get is 9

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$\huge\sf\blue{Given}$

✭ The Number 3645 is divided by a number to make it a perfect cube

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$\huge\sf\gray{To \:Find}$

◈ The number to be divided and the cube root?

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$\huge\sf\purple{Steps}$

$\large\underline{\underline{\sf Concept}}$

To check if a number is a perfect cube we check if the same number repeats trice and if it doesn't we remove the factors which are in excess

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So here we shall first find the factors of the given number,i.e 3645

➳ 3645 = 5 × 3 × 3 × 3 × 3 × 3 × 3

We may observe that here we have an additional 5, so we shall remove it and to do so we have to subtract 3645 by 5

➝ $\sf \dfrac{3645}{5}$

➝ $\sf \red{729}$

Finding its cube root,

»» $\sf \sqrt[3]{729}$

»» 729 = 3 × 3 × 3 × 3 × 3 × 3

»» $\sf \orange{\sqrt[3]{729} = 9}$

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Answer 2

$\huge{ \pmb{ \frak{ \underline{ \color{blue}{❥Answer}}}}}$

$\implies$

Let us factorize the number 3645 .

$\implies$3645 = 5 × 9 × 9 × 9

For a number to be a perfect cube , all the numbers should have triplets .

Here only 9 has a triplet .

And 5 is 2 two times short of a triplet .

Hence we multiply 5×5 both the sides. 

$\implies$3645×5×5=5××5×5×9×9×9

Hence, the smallest number by which 3645 must be multiplied to get a perfect cube is 25.

• I Hope it's Helpful My Friend.