Question

Find the smallest number by which 3645 must be divided so that it becomes a
perfect square. Also, find the square root of the resulting number.
was equal to
​

Answer 1

Answer:

The Prime Factorization :

$3645 = 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 5$

Now, we have to pair the equal factors

$3645 = (3 \times 3) \times (3 \times 3) \times (3 \times 3) \times 5$

So , The number 5 does not have any pair .

Therefore, we must divide 3645 by 5 to make it a perfect square.

$(3 \times 3) \times (3 \times 3) \times (3 \times3 )$

Take one more factor from each pair of L.H.S , so the square root of the new number is

3×3×3 = 27.

Hence, the 27 is the smallest number which can be divided so that it becomes a perfect square.

☆Additional Information☆

The number that is multiplied to itself to get the square number is a square root. There are two methods in maths to find the square root of the square number. They are -

Prime Factorization Method

Long Division Method

Answer 2

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Prime Factorisation:

3645=3x3x3x3x3x3x5

Now, we have to pair the equal factors.

3645=(3x3) x(3x3)x(3x3)x5

The no. 5 doesn't have any pair.

Therefore, we should divide 3645 by 5 to make it a perfect s2.

(3x3) x(3x3)x(3x3)

Take one more factor from each pair of L. H.S,so the root of the new no. =

3x3x3=27

Hence, 27 is the smallest number which can be divided so that it becomes a perfect square.

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