Question

The square root of each of the 5184 is
A.72
B.62
C.74
D.82

Answer 1

Hint: Write the prime factorisation of the given number. Then we will make pairs of the same number. We will take one number from each pair and then we will multiply those numbers to get the square root of the given number.

Complete step-by-step answer:
We will first write the prime factorisation of the number.

2	5184
2	2592
2	1296
2	648
2	324
2	162
3	81
3	9
3	3
3	1

Hence, 5184 can be written as, \[5184 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 3\]
We want to find the square root of 5184,
\[\sqrt {5184} = \sqrt {2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 3} \]
The two same numbers will form a pair.
We will take one factor from each pair and then find their product.
\[2 \times 2 \times 2 \times 3 \times 3 = 72\]
Therefore, the square root of each of the 5184 is 72
Hence, option A is correct.

Note: The square root of a number can alternatively be found by long division method. In the long division method, we first group the numbers from the unit place. Then divide it from the largest number whose square is equal to or just less than the first period. After dividing, bring the next pair down and take the twice of the earlier quotient and extend it with a digit such that the product of the new divisor is equal to or just less than the new dividend.