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The least number by which 216 must be divided to make the result a perfect square, is

Last updated date: 13th Jun 2024
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Hint: In mathematics, a square number or perfect square is an integer that is the square of an integer, in other words, it is the product of some integer with itself. For example, 9 is a square number, since it can be written as $3 \times 3 .$ The usual notation for the square of a number n is not the product $n \times n,$ but the equivalent exponentiation $n^{2}$, usually pronounced as "n squared". The name square number comes from the name of the shape. The unit of area is defined as the area of a unit square type of figurate numbers.

Complete step-by-step answer:
$216=\underline{2\times 2}\times \underline{3\times 3}\times 3$
Here, pairs 2 and 3 are not completed. So, 216 is not a Perfect Square. The number should be divided by $2 \times 3$ to make it a perfect square.
$216 \div 6=36$
Factors of $36=2 \times 2 \times 3 \times 3$
Now, 36 is a perfect square. Hence, the smallest number that should be divided from 216 so that the quotient is a perfect square, is 6.
Hence, the correct answer is Option C.

Note: In mathematics, a square is a product of the whole number with itself. For instance, the product of a number 2 by itself is 4. In this case, 4 is termed as a perfect square. A square of a number is denoted as: $n \times n,$ similarly, the exponential notation of the square of a number is $n^{2}$, usually pronounced as "$n$” squared. Square numbers are usually non- negative.