Question

Find the square root of 42.25 using the division method.

Answer 1

Hint:In these types of questions divide the given number into pairs and then find the square root of the given number by applying the division method.

Complete step-by-step answer:
Using Division Method
First make the pair of numbers in the given number 42.25 using bar over the pair
i.e. \[\overline {42} .\overline {25} \]
Now take the largest number as a divisor whose square root is less than or equal to the extreme left pair
i.e. $\overline {42} $
Let’s take the number 6 as the divisor
Now dividing $\overline {42} $ by 6
Here the quotient is 6 and the remainder is 6
Placing decimal after 6 in quotient
Now bring the next bar $\overline {25} $to the right of the remainder
Now the new dividend is 625
Let’s take number 125 as a divisor for the new dividend
Dividing 625 by 125
Here the quotient is 5 and the remainder is 0
Since the remainder is 0 and the quotient is 6.5
This means 6.5 is the square root of 42.25.

Note: In division method divide the number into pairs from the once digit and divide the pairs with the nearest prime number to obtain the square root.