Question

the least number by which 7092 must be divided so that the quotient is a perfect square is the​

Answer 1

We have to find the smallest number by which 7092 could be divided to obtain a perfect square number as the quotient. Let's go step by step.

➭ We begin with the prime factorization of 7092 first. We need to find prime numbers that do not exist in pairs while factorizing the number.

$\Large{ \begin{array}{c|c} \tt 2 & \sf{ 7092} \\ \cline{1-2} \tt 2 & \sf { 3546} \\ \cline{1-2} \tt 3 & \sf{ 1773} \\ \cline{1-2} \tt 3 & \sf{ 591} \\ \cline{1-2} \tt 197 & \sf{ 197 }\\ \cline{1-2} & \sf{ 1} \end{array}}$

• 7092 = 2 x 2 x 3 x 3 x 197

➭ The number 197 does not exist in pair. Thus, we divide 7092 by 197. This also means we are removing 197 from the factors.

• 2² x 3² = 4 x 9 = 36

➭ For the answer,

• The smallest number that could divide 7092 and give a perfect square =  197
• The perfect square number obtained = 36

Therefore, the least number by which 7092 must be divided so that the quotient is a perfect square is 197.

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