Question

c. 11200 find the samallest number should be divided so the quotient is perfect square​

Answer 1

Step-by-step explanation:

by prime factorisation method , we get

7 is a smallest number , that should be divided by 11200 to get a perfect square

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Answer 2

Question :-

Find the smallest number by which 11200 should be divided so that the quotient is a perfect square.​

Answer :-

7

Step-by-step explanation:

Let’s find out the prime factor of given number to  find the smallest number which should be divided so that the quotient is a perfect square

$\begin{array}{r | l} 2 & 11200 \\ \cline{1-2} 2 & 5600 \\ \cline{1-2} 2 & 2800 \\ \cline{1-2} 2 & 1400 \\ \cline{1-2} 2 & 700 \\ \cline{1-2} 2 & 350 \\ \cline{1-2} 5 & 175 \\ \cline{1-2} 5 & 35 \\ \cline{1-2} 7 & 7 \\ \cline{1-2} 1 & 1\end{array}$

$\sf{}Therefore,$

$\sf{}Factors\ of\ 11200 =\underbrace{2\times 2}\times \underbrace{ 2 \times 2} \times \underbrace{2 \times 2}\times \underbrace{5 \times 5}\times 7$

7 has no pair so if we will divide it by 7 then quotient become a perfect square.

Hence,7 is the smallest number by which should be divided so the quotient is perfect square.