Question

Find the square root of the following numbers corrects up to 2 decimal places.
a) 70
b) 89
c) 134
d) 526

Answer 1

We will use the long division method to find the square root of the given numbers, 70, 89, 134, and 526. In the long division method, we will first pair the given numbers, and then we will think of the largest number whose square is equal to or just less than the first group. Then we will subtract the product with the divisor and bring down the new group. Then the new divisor is obtained by taking two times the quotient. The quotient obtained will be our required root.

Complete step-by-step answer:
It is given in the question that we have to find the square root of the following given numbers correct up to 2 decimal places, 70, 89, 134, and 526. We will use the long division method to find the square root of the given number up to their two decimal points. While performing the long division method, we have to follow the following steps.
Step 1 - We will first group the digits in pairs and here each pair is called a period.
Step 2 - We will put pairs of zero after number as a separate period, as in 70, we will put $\overline{70.}\overline{00}\overline{00}$.
Step 3 - We will think of the largest number whose square is equal to or just less than the first period. We will take this number as our divisor and the quotient.
Step 4 - We will subtract the product of the divisor and quotient from the first period and then we will bring down the next period as a dividend.
Step 5 - Now, we will take the divisor by taking two times the quotient and we will select it in such a way that the product of the new divisor and the new digit are equal to or less than the new dividend.
Step 6 - We will repeat steps 1, 2, 3, 4, 5 till all the periods have been consumed.
The obtained quotient will be our required square root of the given number.
a) 70. We have the first number given as 70. So, on performing long division method for it, we get,

Thus, $\sqrt{70}=8.36$.
b) 89. We have the second number as 89. So, on performing long division method, we get,

Thus, $\sqrt{89}=9.43$.
c) 134. We have the next number as 134. So, we get,

Thus, we get, $\sqrt{134}=11.57$.
d) 526. We have the last number as 526. So, on performing long division, we get,

Thus, we get, $\sqrt{526}=22.93$

Note: This is one of the most basic questions on finding the square root, but the majority of students make a mistake while performing the long division method. They may take the wrong value as the quotient or they may subtract the wrong product with the period, which would lead to a wrong answer.