Question

Find the square root of the given decimal number: \[84.64\].

Answer 1

Hint:
Here, we will find the square root of the given number using the long division method by grouping 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 \[84.64\].
Since the given number is a larger number with 4 digits, we will find the square of \[84.64\] using the 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 \[84.64\].
\[\overline {84} {\text{ .}}\overline {64} \]
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 \[84.64\] in long division method is \[9.2\].
Since the remainder of the square root of \[84.64\] in long division method is 0, the final value is \[9.2\].

Thus, the square root of \[84.64\] is \[9.2\] by long division method.

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.
\[9.2 \times 9.2 = 84.64\]
Hence, \[9.2\] is the square root of the number \[84.64\].