Aptitude - Square Root and Cube Root - Discussion

| 21 36 66
2| 21 18 33
2| 21 9. 33
3| 7. 3. 11.

==> 2*2*3*3*7*11.
=> 4*9*77,
=> 36*77,
=> 2772.

To make perfect square means, Make all digits square.

Already we have a square for 2 and 3,
Remaining make square i.e., 7^2. 11^2,

So, Totally....2772*11*7=213444.

Let's solve it by option elimination.

21 divisibility test number should be divisible by 7 and 3,
36 divisibility test number should be divisible by 9 and 4,
66 divisibility test number should be divisible by 11 and 6,
So option A and C are divisible by 11 and B and d are not so discard B and D.
So option C is not a perfect square so the correct answer is Option A.

Why we have multiplied 2 3 7 11 square? Please explain me.

How? Please explain me.

Since 213444 is divisible by all of the three number i.e. 21, 36, 66 so its the answer. We don't even have to see the second option.

L.C.M. of 21, 36, 66 = 2772.
Now, 2772 = 2 x 2 x 3 x 3 x 7 x 11.
To make it a perfect square, it must be multiplied by 7 x 11.
So, required number = 22 x 32 x 72 x 112 = 213444.

How to square 7 & 11? Can anyone explain in shortcut method?

Why should we square 7 and 11? Please explain to me.

Remember it's the least common factor we looking for 21, 36 and 66.

Find the Lcm = 3 * 2 * 7 * 6 * 11 = 3 * 2 * 7 * 3 * 2 * 11 = 2772 (the 3*2 after 7 is a perfect square to replace the 6 that's in the initial equation coz 3*2 is 6).

3 and 2 are the highest common factors while 7 and 11 are the least because they both appear once. So multiply the Lcm (2772) with 7 and 11 and you get your answer;
That is 2772 * 7 * 11 = 213444.

Hope this helped someone understand better.

Why should we multiply by 7 and 11? Please tell me.