Question

Find the square root of
(a)$5929$
(b)$3969$
(c) $8836.$

Answer 1

Hint: We will do prime factorization of each value. Thereafter we will make a pair of prime factors of the numbers. Further we will multiply the number that we choose in pairs. Then we will multiply to get an answer.


Complete step by step solution:
(a) $5929$ is an odd number. Therefore, it is divisible by Prime odd number. We take $7$ an odd number then, $11$

7	5929
7	847
11	121
11	11
	1

Square root of \[\sqrt {5929} = \sqrt {\overline {7 \times 7} \times \overline {11 \times 11} } \]
\[7 \times 11 = 77\,\,\,answer.\]
(b) 3969 is an odd number therefore, it is divisible by only an odd prime number. So we take an odd prime number of 3 after that 7.

3	3969
3	1323
3	441
3	147
7	49
7	7
	1

Square root of \[\sqrt {3969} = \sqrt {\overline {3 \times 3} \times \overline {3 \times 3} \times \overline {7 \times 7} } \]
\[ = 3 \times 3 \times 7\]
\[ = 63\,\]ans.
(c) 8836 is an even number. Therefore it is divisible by only even prime number i.e. 2 then 47

2	8836
2	4418
47	2209
47	47
	1

Square root of \[\sqrt {8836} = \sqrt {2 \times 2 \times 47 \times 47} \]
 \[ = 2 \times 47 = 94\,\,\]ans.

Note: Remember the given number is even or odd. If it is odd then divide the given number by the odd numbers and if it is an even then divide the given number by the even numbers.