Question

The square root of 15129
A) 123
B) 223
C) 113
D) 213

Answer 1

Hint:
Here, we will find the square root of the given number using the long division method by the group the digits in pairs starting from the right to left, Then we will now take the largest number whose square is equal to or just less than the first pair. Then subtract the product of the obtained divisor and the quotient from the first pair and bring down two the new pair. We will continue this process until the remainder is zero. Then the obtained quotient will be the required square root.

Complete step by step solution:
We are given that the number is 15129.
Since the given number is a larger number with 5 digits, we will find the square of 15129 using long division method.
We know that the square root of a given number using division method is calculated by the group the digits in pairs starting from the right to left, Then we will now take the largest number whose square is equal to or just less than the first pair. Then subtract the product of the obtained divisor and the quotient from the first pair and bring down two the new pair. We will continue this process until the remainder is zero.

First, we will separate the digits by taking bars from right to left once in two digits of the given number 15129.
\[\overline 1 {\text{ }}\overline {51} {\text{ }}\overline {29} \]
Now we will find the square root of the above pairs using the long division method.

We know that the quotient of the square root of 15129 in long division method is 123.
Since the remainder of the square root of 15129 in long division method is 0, the final value is 123.

Thus, the square root of 15129 is 123 by long division method.
Hence, option A is correct.

Note:
Note: In solving these types of questions, you should be familiar with the steps to find the square root using the long division method. Some students separate the digits by taking bars from left to right once in two digits, which is wrong. We can also verify our solution by finding the square of the obtained square root. Also, we are supposed to write the values properly to avoid any miscalculation.