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Submitted By : Charchit
Submitted To : Ms. Shikha
Class : 8th C
Roll No. : 4
Admn. No. : 7026
In earlier classes, We Have learnt about integral
exponents of rational numbers. When the exponent of
natural number is 2, the number obtained is called a
square number or a perfect square.
For example: 22, 52, 92 etc.
In general, if natural number m can be
expressed as n2 , when n is also a natural
number, then m is a square number.
52 = 25
62 = 36
The numbers 1,4,9,16………are square numbers.
These are also called perfect squares.
Properties of square numbers
Property 1- A number having 2,3,7or8 at unit’s
place is never a perfect square.
Eg: Numbers 152, 7693, 1437, 88888
aren’t perfect squares.
Property 2- Squares of even numbers is always
even and of odd numbers will always
odd. Eg: 102=100, 52= 25.
Property 3- If a square of a number will ends in 0
will also ends in 0, if it will 5 also ends
in 5. Eg:52=25, 102=100.
Property 4- If a number has 1 or 9 in its ones
place, its square will end in 1.
Eg: 12=1, 92=81
The square of a number x is that a
number which when multiplied by
itself gives x as the product and the
square root of x is denoted by .
Finding square root of a
squareIn order to find the square root of a perfect square,
resolve it into prime factors; make pairs of similar
factors; and take the product of prime factors,
choosing one out from each pair.
1. THE METHOD OF REPEATED
2. PRIME FACTORIZATION
3. LONG DIVISION METHOD
Methods to find Square Root
36 – 1 = 35
35 – 3 = 32
32 – 5 = 27
27 – 7 = 20
20 – 9 = 11
11 – 11 = 0
So the square root of 36 is equal to the
number of steps that are 6. So the square
root of 36 is 6.
Step 1- Obtain the given number.
Step 2- Write the Prime Factors in pairs.
Step 3- Group the Prime Factors in Pairs.
Step 4- Write the numbers as square root of prime factors.
Step 5- Take one factor from each pair.
Step 6- Find the product of factors obtained in Step 5.
Step 7- The product obtained in Step 6 is the required
Step1- Obtain the number whose square root is to
Step2- Place bars over every pair of digits starting
with the units digits. Also place a, bar on one
digit (if any) not forming a pair on the extreme
left. Each pair and the remaining one digit (if
any) on the extreme left is called a period.
Step3- Think of the largest number whose square is less
than or equal to the first period. Take this
number as the divisor and the quotient.
Step4- Put the quotient above the period and write the
product of divisor and quotient just below the
Step5- Subtract the product of divisor and quotient from the first
period and bring down the next period to the right of the
remainder. This becomes the new dividend.
Step6- Double the quotient as it appears and enter it with a blank
on the right for the next digit, as the next possible divisor.
Step7- Think of a digit, to fill the blank in step 6, in such a way
that the product of new divisor and this digit is equal to or
just less than the new dividend obtained in step 6.
Step8- Subtract the product of the digit chosen in step 7 and the
new divisor from the dividend obtained in step 6 and bring
down the next period to the right of the remainder. This
becomes new dividend.
Step9- Repeat steps 6, 7 and 8 till all periods have been taken up.
Step10- Obtain the quotient as the square root of the given