Squares and Square Roots

L.C.M of $2352=2^2\times 2^2\times 7^2\times 3$
To make $2352$ a perfect square it must be multiplied by $3$

Let the number in the given problem be x. Then, according to the problem 

$12 \times 12 =144, 12^2 = 144$. 

$144$ is a square of number $12$.

Therefore, option A is the correct answer.

The square of the number $78$ is $6084$

we know 

Square of a number means multiplying a number with the same number.

Square of $17\times 17 =289$.

Therefore, option B is the correct answer.

Square of  a number means multiply a number with the same number.

$22 \times 22= 22^2  = 484$

Thus the square of number $22$ is $484$.

Therefore, option C is the correct answer.

$59^{2} = 59 \times 59 = 3481$

We have 2352 =  $ \displaystyle \underline{2\times 2}\times \underline{2\times 2}\times 3\times \underline{7\times 7} $
As the prime factor 3 has no pair 2352 is not a perfect square 

$112^2 = (100 + 12)^2$
$a = 100, b = 12$
$= a(a + b) + b(a + b)$
$= 100(100 + 12) + 12(100 + 12)$
$= 100^2 + 1200 + 1200 + 12^2$
$= 10000 + 2400 + 144$
$= 12544$
The missing number is 144.

Step 1 :Multiply ten's digit with its next number.
$2 \times (2 + 1) = 2\times 3 = 6 ---(1)$
Step 2 : Find the square of unit's digit: 5
$5^2 = 25 ----(2)$
Combining (1) and (2), we get
$25 \times 25 = 625$
$6 $ is the missing number.

Multiply ten's digit with its next number.
$7 \times (7 + 1) = 7 \times 8 = 56 ---(1)$
Find the square of unit's digit: $5$
$5^2 = 25$ ----(2)
Combining (1) and (2), we get
$5625 = 75 \times75$
So, $6$ is the missing number.

$\dfrac{9}{10}$$\times$$\dfrac{9}{10}$ $=$ $\dfrac{81}{100}$