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Hint: We are asked here to find the square root by using the division method. So, we’ll follow the method step wise. We’ll start with grouping the digits of a number in two starting from the units place and follow the next steps accordingly.

Complete step-by-step answer:

We can group the number 448 in two groups (also called as period) i.e. 44 and 89

44 is the first period and 89 is the second.

Now think of the largest number whose square is equal or smaller than the first period. Take this number as the divisor and also as the quotient.

So, we have \[{6^2} = 36\]

Now, subtract the product of the divisor and Quotient from the first period and bring down the next period to the right of the remainder. This becomes the new dividend i.e. 12

Now, the divisor is obtained by taking two times the quotient and annexing it with a digit which is also taken as the next digit of the quotient, chosen in such a way that the product of the new divisor and this digit is equal to or just less than the new dividend. i.e 7

Note: To find the square root of a perfect square by using the long division method is easy when the numbers are very large since, the method of finding their square roots by factorization becomes lengthy and difficult.

Complete step-by-step answer:

We can group the number 448 in two groups (also called as period) i.e. 44 and 89

44 is the first period and 89 is the second.

Now think of the largest number whose square is equal or smaller than the first period. Take this number as the divisor and also as the quotient.

So, we have \[{6^2} = 36\]

Now, subtract the product of the divisor and Quotient from the first period and bring down the next period to the right of the remainder. This becomes the new dividend i.e. 12

Now, the divisor is obtained by taking two times the quotient and annexing it with a digit which is also taken as the next digit of the quotient, chosen in such a way that the product of the new divisor and this digit is equal to or just less than the new dividend. i.e 7

67 | |

6 | $\;\;\;\:\overline {44} \overline {89}\\-36$ |

127 | $\;\;\;\;\;\,889\\-\;\;889$ |

$\;\;\;\;\;\;0$ |

Note: To find the square root of a perfect square by using the long division method is easy when the numbers are very large since, the method of finding their square roots by factorization becomes lengthy and difficult.