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Square root of decimal numbers by long division method Video Lecture - Class 8
FAQs on Square root of decimal numbers by long division method Video Lecture - Class 8
| 1. How do you find the square root of a decimal number using the long division method? |  |
Ans. To find the square root of a decimal number using the long division method, follow these steps:
1. Group the digits of the decimal number into pairs, starting from the decimal point and moving towards the left.
2. Find the largest whole number whose square is less than or equal to the leftmost group. Write this number as the quotient's first digit.
3. Subtract the product of the quotient's first digit and the divisor from the leftmost group.
4. Bring down the next group of digits to the right of the remainder obtained in the previous step.
5. Double the quotient's first digit and find the largest digit to be placed in the quotient's second digit such that when the new divisor (formed by the quotient's first digit and the new digit) is multiplied by this digit, the product is less than or equal to the new dividend.
6. Repeat steps 3 to 5 until all the decimal places are obtained in the quotient.
| 2. Can the long division method be used to find the square root of any decimal number? | |
Ans. Yes, the long division method can be used to find the square root of any decimal number. By following the steps of the long division method accurately, the square root of a decimal number can be determined.
| 3. Is the long division method the only way to find the square root of a decimal number? | |
Ans. No, the long division method is not the only way to find the square root of a decimal number. There are other methods such as the estimation method, using a calculator or computer software, or using mathematical formulas specifically designed for certain types of decimal numbers.
| 4. Are there any limitations or drawbacks to using the long division method for finding square roots of decimal numbers? | |
Ans. One limitation of the long division method is that it can be time-consuming and require complex calculations, especially for decimal numbers with a large number of digits. Additionally, the method may not be suitable for finding square roots of extremely large or small decimal numbers, as it may become impractical to perform the calculations manually.
| 5. How can the square root of a decimal number be verified after using the long division method? | |
Ans. After finding the square root of a decimal number using the long division method, the result can be verified by squaring the obtained square root. If the square of the square root equals the original decimal number, then the calculation is correct. However, if the square does not match the original decimal number, then an error may have occurred during the long division method calculation.
Text Transcript from Video
hi I am Anita today I am going to teach
you how to find the square root of
decimal numbers suppose I am taking a
number as four seventy seven point four
two two five in decimal numbers there
are two parts this part is known as
integral part and this part is known as
decimal part
now finding the square root of suppose
this number for seventy seven point four
two to five
first you have to put the bar on
integral part from unit desert like this
and in decimal part from 10th place like
this now think of a largest number whose
square is equal to 4 or less than 4 so I
am taking 2 so 2 times 2 is 4 now my
quotient is 2 so I am adding quotient
over here during square root you have to
take the numbers in pairs so I am taking
77 down sorry 2 plus 2 is 4
now think of a number in the
fill-in-the-blank in such a way that the
product of new divisor and this digit is
equal to 77 or less than 77 so I am
taking 2 so 42 times 2 which is 84 which
is greater than 77 so I am considering 1
so 41 times 1 is 41 now my new quotient
is 1 so I am adding 1 over here so it
becomes 42 and I am subtracting 41 from
77 so I will get 36
now there is a decimal so I am putting a
decimal on the top and taking the next
pair down which is 42 now think of a
largest num think of a number in the
fill-in-the-blank
in such a way that the product of new
divisor and this digit is equal to 3600
and 42 or less than 3642
so I am considering four to seven
multiplying it by seven so I will get 7
times 7 is 49 4 carry 7 times 2 is 14
plus 4 18 1 carry 7 times 4 is 28 plus
129 but I think this number is less than
3642
so I am considering next number as 8 so
for 28 times 8 8 times 8 is 64 6 carry 8
times 2 is 16 plus 6 22 to carry 8 times
4 is 32 plus 2 which is 34 so I am
putting 8 over here
8 here and 3424 here now my new quotient
is 8 so I'm adding 8 over here so I'll
get 4 36 and when I am doing subtraction
I will get 12 minus 4 is 8 4 minus 3 is
1 6 minus 4 is 2
now I'm taking next pair down 25 now
think of a number in the fill in the
blanks in such a way that the product of
new divisor and this rigid is equal to
or less than 2 1 8 2 5 so I am taking 5
so 4 3 6 5 times 5 I will get 4 5 times
5 is 25 to carry 5 times 6 is 30 plus 2
32 3 carry 5 times 3
fifteen plus three eighteen one carry
five times four is 20 plus one 21
Wow I got it so I am putting Phi on the
top 2 1 a 2 Phi here and Phi in this
fill in the blanks so after doing
subtraction I will get 0 as a remainder
so the square root of 4 seventy seven
point four two two five is twenty one
point eight five now let us take and
another example as I am taking one small
example here suppose we have to find the
square root of six point two five now
here I am making the pair first of
integral part then of decimal part now
think of a largest number whose square
is equal to 4 or less than sorry equal
to 6 or less than 6 so I am taking 2 so
2 times 2 is 4 my quotient is 2 so I'm
adding quotient over here and subtract 4
from 6 so I will get 2 now there is a
decimal so I'm putting a decimal on the
top and taking the pair down so 2 to 5
now think of a number in fill in the
blank in such a way that the product of
new divisor and this digit is equal to
or less than 2 to 5 so I am considering
45 multiplied by 5 so I'll get 5 times 5
is 25 to carry 5 times 4 is 20 plus 225
yes so it's y
- - why so the remainder is zero so from
this I can say that the square root of
six point two five is two point five for
more details you can log on to
www.nasa.gov
as - mat.com thank you
you how to find the square root of
decimal numbers suppose I am taking a
number as four seventy seven point four
two two five in decimal numbers there
are two parts this part is known as
integral part and this part is known as
decimal part
now finding the square root of suppose
this number for seventy seven point four
two to five
first you have to put the bar on
integral part from unit desert like this
and in decimal part from 10th place like
this now think of a largest number whose
square is equal to 4 or less than 4 so I
am taking 2 so 2 times 2 is 4 now my
quotient is 2 so I am adding quotient
over here during square root you have to
take the numbers in pairs so I am taking
77 down sorry 2 plus 2 is 4
now think of a number in the
fill-in-the-blank in such a way that the
product of new divisor and this digit is
equal to 77 or less than 77 so I am
taking 2 so 42 times 2 which is 84 which
is greater than 77 so I am considering 1
so 41 times 1 is 41 now my new quotient
is 1 so I am adding 1 over here so it
becomes 42 and I am subtracting 41 from
77 so I will get 36
now there is a decimal so I am putting a
decimal on the top and taking the next
pair down which is 42 now think of a
largest num think of a number in the
fill-in-the-blank
in such a way that the product of new
divisor and this digit is equal to 3600
and 42 or less than 3642
so I am considering four to seven
multiplying it by seven so I will get 7
times 7 is 49 4 carry 7 times 2 is 14
plus 4 18 1 carry 7 times 4 is 28 plus
129 but I think this number is less than
3642
so I am considering next number as 8 so
for 28 times 8 8 times 8 is 64 6 carry 8
times 2 is 16 plus 6 22 to carry 8 times
4 is 32 plus 2 which is 34 so I am
putting 8 over here
8 here and 3424 here now my new quotient
is 8 so I'm adding 8 over here so I'll
get 4 36 and when I am doing subtraction
I will get 12 minus 4 is 8 4 minus 3 is
1 6 minus 4 is 2
now I'm taking next pair down 25 now
think of a number in the fill in the
blanks in such a way that the product of
new divisor and this rigid is equal to
or less than 2 1 8 2 5 so I am taking 5
so 4 3 6 5 times 5 I will get 4 5 times
5 is 25 to carry 5 times 6 is 30 plus 2
32 3 carry 5 times 3
fifteen plus three eighteen one carry
five times four is 20 plus one 21
Wow I got it so I am putting Phi on the
top 2 1 a 2 Phi here and Phi in this
fill in the blanks so after doing
subtraction I will get 0 as a remainder
so the square root of 4 seventy seven
point four two two five is twenty one
point eight five now let us take and
another example as I am taking one small
example here suppose we have to find the
square root of six point two five now
here I am making the pair first of
integral part then of decimal part now
think of a largest number whose square
is equal to 4 or less than sorry equal
to 6 or less than 6 so I am taking 2 so
2 times 2 is 4 my quotient is 2 so I'm
adding quotient over here and subtract 4
from 6 so I will get 2 now there is a
decimal so I'm putting a decimal on the
top and taking the pair down so 2 to 5
now think of a number in fill in the
blank in such a way that the product of
new divisor and this digit is equal to
or less than 2 to 5 so I am considering
45 multiplied by 5 so I'll get 5 times 5
is 25 to carry 5 times 4 is 20 plus 225
yes so it's y
- - why so the remainder is zero so from
this I can say that the square root of
six point two five is two point five for
more details you can log on to
www.nasa.gov
as - mat.com thank you
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Oct 28, 2024 Last updated |
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