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square root of 10201 by long division

Jul 21, 2024

square root of 10201 by long division

Solution by Steps

step 1

To find the square root of 10201 using long division, we first pair the digits from right to left: (10)(20)(1)

step 2

Find the largest number whose square is less than or equal to the first pair (10). This number is 3, since

3^2 = 9

step 3

Subtract

9

from

10

to get

1

. Bring down the next pair (20) to get

120

step 4

Double the divisor (3) to get

6

. Find the largest digit

x

such that

6x \cdot x \leq 120

. The digit is 1, since

61 \cdot 1 = 61

step 5

Subtract

61

from

120

to get

59

. Bring down the next pair (01) to get

5901

step 6

Double the current quotient (31) to get

62

. Find the largest digit

y

such that

62y \cdot y \leq 5901

. The digit is 9, since

629 \cdot 9 = 5661

step 7

Subtract

5661

from

5901

to get

240

. Since there are no more pairs to bring down, the process stops here

step 8

The quotient obtained is

101

, and the remainder is

240

. Therefore, the square root of

10201

101

Answer

The square root of 10201 is 101.

Key Concept

Long Division Method for Square Roots

Explanation

The long division method involves pairing digits, finding the largest possible digits for each step, and subtracting to find the remainder. This process is repeated until all pairs are used.