Question

find the square root of 237.615 correct to three decimal places

Answer 1

Hi,

Square root:

The square root of a number is that number,

whose square is equal to the given number.

Long division method:

1 ) Group the digits in pairs, starting with the

digit in the units pkace .Each pair and the

remaining digit ( if any ) is called period.

2) Find the largest number whose square is

equal to just less than the first period.Take

this number as the divisor and as the quotient.

3) Subtract the product of the divisor and the

quotient from the first period and bring down

the next period to the rightnof the remainder .

This becomes the new dividend.

4) Now, the new divisor is obtained by taking

two times the quotient and annexing with it

a suitable digit which is also taken as the next

digit of the quotient chose in such a way that

the product of the new divisor and this digit is

equal to or just less than the new dividend.

5) Repeat steps 2,3 and 4 till the periods

have been taken up.

1 ) 2 37 . 61 50 00 00 (15.4147
1
______________
25)137
125
__________
304)1261
1216
__________
3081)14550
13081
____________
30824)146900
123296
_____________
308287) 2360400
2158009
_______________
202391


Therefore,

Sqrt(237.615) = 15.4147

= 15.415

( corrected to 3 decimal places )

I hope this helps you.

:)

Answer 2

1 ) Group the digits in pairs, starting with the

digit in the units place .Each pair and the

remaining digit ( if any ) is called period.

2) Find the largest number whose square is

equal to just less than the first period.Take

this number as the divisor and as the quotient.

3) Subtract the product of the divisor and the

quotient from the first period and bring down

the next period to the rightnof the remainder .

This becomes the new dividend.

4) Now, the new divisor is obtained by taking

two times the quotient and annexing with it

a suitable digit which is also taken as the next

digit of the quotient chose in such a way that

the product of the new divisor and this digit is

equal to or just less than the new dividend.

5) Repeat steps 2,3 and 4 till the periods

have been taken up.

1 ) 2 37 . 61 50 00 00 (15.4147

1

______________

25)137

125

__________

304)1261

1216

__________

3081)14550

13081

____________

30824)146900

123296

_____________

308287) 2360400

2158009

_______________

202391

Therefore,

Sqrt(237.615) = 15.4147

= 15.415 Ans( corrected to 3 decimal places )