Question

Find the smallest whole number by which 192 should be

multiplied so as to get a perfect square. Also find the square root

of the new number.
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Answer 1

since this is a "should be multiplied/divided" type question, we will proceed with prime factorisation method

(if it was " should be added/subtracted" type question, we would proceed with long division method)

192 = 2 x 2 x 2 x 2 x 2 x 2 x 3

-------. ------. -------

we see that the twos are in pairs but the three is alone. we need to make pairs for the number to be perfect square. If we multiply the number by 3, we would get additional three which will make pair with the alone 3 and number will be perfect square.

so the answer is 3

the square root will be

= 2 x 2 x 2 x 3 = 24