Question

Find the smallest natural numbers by
which 5808
should be divided to make
it a perfect Square. Also find the
number whose Square is the resulting number​

Answer 1

Answer :-

• The smallest natural number by which 5808 should be divided to make it a perfect square is 3.

• 44 is the number whose square is the resulting number.

To find :-

• The smallest natural number by which 5808 should be divided to make it a perfect square.

• The number whose square is the resulting number.

Solution :-

• First, let's find the prime factors of 5808 by prime factorisation!

Prime factorisation of 5808 :-

$\begin{array}{c | c} \underline2 & \underline{5808} \\ \underline2&\underline{2904} \\ \underline2 &\underline{1452} \\ \underline2&\underline{726} \\ \underline3&\underline{363} \\\underline{11}&\underline{121} \\ \underline{11}&\underline{11} \\ &1 \end{array}$

The given number is 5808.

It can be expressed as :-

$\sf \underbrace{2 \times 2} \times \underbrace{2 \times 2} \times 3 \times \underbrace{11 \times 11}$

Since :-

• 3 is left unpaired, therefore, to make 5808 a perfect square, it should be divided by 3.

Hence :-

• The smallest natural number by which 5808 should be divided to make it a perfect square is 3.

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Now,

• 5808 ÷ 3 = 1936.

So :-

• We now have to find the number whose square is 1936.

Hence,

• Let's find the prime factors of 1936 by prime factorisation!

Prime factorisation of 1936 :-

$\begin{array}{c | c} \underline{2} & \underline{1936} \\ \underline{2}& \underline{968} \\ \underline2 & \underline{484} \\ \underline2&\underline{242} \\\underline{11}& \underline{121} \\ \underline{11}& \underline{11} \\ & 1\end{array}$

Now,

$\sf1936 = \underbrace{2 \times 2} \times \underbrace{2 \times 2}\times \underbrace{ 11 \times 11}$

$\sf1936 = ( {2}^{2} ) \times ( {2}^{2}) \times ({11}^{2} )$

$\sf1936 = (2 \times 2 \times 11)^{2}$

$\sf1936 = ( {44}^{2} )$

Therefore :-

• 44 is the number whose square is 1936 (the resulting number)

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