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Finding square root of 4 digit number using division method - Square & Square Roots Video Lecture - Class 8
FAQs on Finding square root of 4 digit number using division method - Square & Square Roots Video Lecture - Class 8
| 1. How do you find the square root of a 4-digit number using the division method? |  |
Ans. To find the square root of a 4-digit number using the division method, follow these steps:
1. Group the digits of the given number into pairs, starting from the unit's place.
2. Find the largest number whose square is less than or equal to the first pair of digits. This number will be the first digit of the square root.
3. Subtract the square of this digit from the first pair of digits and bring down the next pair of digits.
4. Double the first digit of the square root and assume it as the divisor.
5. Find the largest possible digit to be placed at the right of the divisor, such that the product of the divisor and this digit is less than or equal to the dividend.
6. Write this digit as the second digit of the square root and place it on top of the rightmost digit of the dividend.
7. Multiply the divisor (two-digit number) by the second digit of the square root, write the product below the dividend, and subtract it.
8. Bring down the next pair of digits and repeat steps 5 to 7 until all the digits have been brought down.
9. The resulting quotient will be the square root of the given 4-digit number.
| 2. Can the division method be used to find the square root of any number? | |
Ans. The division method can be used to find the square root of any positive number, including 4-digit numbers. However, for very large numbers, the manual division method can become time-consuming and challenging. In such cases, it is more efficient to use calculators or computer algorithms to find the square root.
| 3. What is the significance of grouping the digits in pairs while using the division method? | |
Ans. Grouping the digits in pairs while using the division method is significant because it simplifies the process of finding the square root. By pairing the digits, we can work with two-digit numbers instead of single digits, making the division process more manageable and easier to perform mentally or manually.
| 4. Are there any shortcuts or alternative methods to find the square root of a 4-digit number? | |
Ans. Yes, there are alternative methods to find the square root of a 4-digit number. One such method is the prime factorization method, where the given number is expressed as a product of its prime factors. The square root is then obtained by taking one factor from each pair of prime factors. However, the division method is commonly taught in schools and provides a systematic approach to finding square roots.
| 5. Can the division method be used to find the square root of decimal numbers or negative numbers? | |
Ans. No, the division method is not suitable for finding the square root of decimal numbers or negative numbers. The division method is specifically designed for positive whole numbers. For decimal numbers, other methods like the long division method or estimation techniques need to be applied. Similarly, for negative numbers, complex numbers and the concept of imaginary numbers come into play.
Text Transcript from Video
okay in this video let us look at
another example of four digits and then
we apply the division method to find out
the square root of a number so let us
say we will take the number 4 0 9 6 and
we are supposed to find out the square
root of this number so the step one is
to make pairs of numbers starting from
units place so in this case the first
pair is 96 and then the second pair is
40 so that is step one step two we begin
with division ok and so what in the
first case now in this case we always
have to take a pair so the first pair
that we have is 4 P now we have to find
out a number a square number a number
which whose square is either equal to or
less than 40 so now it is very useful
for this method that you have at least
the squares of one to ten you just
remember them in your head and you
should not be having to calculate them
when you are working out this so that's
quite a helpful now in this case I can
straight away say that the square of 6 6
squared is 36 now if I take 7 squared
it gives me 49 which is greater than 4 P
what is what we have over here so we
will take the first digit of the
quotient as 6 or the first number that
we are going the first we have the first
digit as 6 now 6 times 6 gives us 36 we
write it down okay now we do the
subtraction so 40 minus 6 gives us 4 and
then you also get 96 down so we have 496
now the third step would be to double
this 6 so when we double 6 we get 12 and
write down a blank position over here so
1/2 times blank now we have to find out
a number over here such that when you
multiply that now
with this the number that is formed this
one to again let me just show it over
here so we have one two let's say that
digit is a multiplied by a it should be
equal to this number okay equal to or
less than this number and if you
remember the secret tip that I gave you
is to kind of just try out the numbers
whose square ends in six so if you think
of it which numbers square end in six so
the first one for example six ends 6
squared is 36 4 squared is 16 so we can
try let us say we will say a equals 4 so
this blank is actually a equals 4 so we
have 1 24 multiplied by 4 and when you
do this 4 times 4 is 16
you carry it over 1 4 times 2 is 8 and 1
you get 9 and 4 times 1 is 4 so you got
496 so what we do is we write 4 over
here 1 24 multiplied by 4 it gives you
496 which then gives you the remainder
as 0 so in this case we can say that the
square root of 4 0 9 6 is 64
so that was another example of finding
out square root of a number using the
division method
another example of four digits and then
we apply the division method to find out
the square root of a number so let us
say we will take the number 4 0 9 6 and
we are supposed to find out the square
root of this number so the step one is
to make pairs of numbers starting from
units place so in this case the first
pair is 96 and then the second pair is
40 so that is step one step two we begin
with division ok and so what in the
first case now in this case we always
have to take a pair so the first pair
that we have is 4 P now we have to find
out a number a square number a number
which whose square is either equal to or
less than 40 so now it is very useful
for this method that you have at least
the squares of one to ten you just
remember them in your head and you
should not be having to calculate them
when you are working out this so that's
quite a helpful now in this case I can
straight away say that the square of 6 6
squared is 36 now if I take 7 squared
it gives me 49 which is greater than 4 P
what is what we have over here so we
will take the first digit of the
quotient as 6 or the first number that
we are going the first we have the first
digit as 6 now 6 times 6 gives us 36 we
write it down okay now we do the
subtraction so 40 minus 6 gives us 4 and
then you also get 96 down so we have 496
now the third step would be to double
this 6 so when we double 6 we get 12 and
write down a blank position over here so
1/2 times blank now we have to find out
a number over here such that when you
multiply that now
with this the number that is formed this
one to again let me just show it over
here so we have one two let's say that
digit is a multiplied by a it should be
equal to this number okay equal to or
less than this number and if you
remember the secret tip that I gave you
is to kind of just try out the numbers
whose square ends in six so if you think
of it which numbers square end in six so
the first one for example six ends 6
squared is 36 4 squared is 16 so we can
try let us say we will say a equals 4 so
this blank is actually a equals 4 so we
have 1 24 multiplied by 4 and when you
do this 4 times 4 is 16
you carry it over 1 4 times 2 is 8 and 1
you get 9 and 4 times 1 is 4 so you got
496 so what we do is we write 4 over
here 1 24 multiplied by 4 it gives you
496 which then gives you the remainder
as 0 so in this case we can say that the
square root of 4 0 9 6 is 64
so that was another example of finding
out square root of a number using the
division method
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