D.A.V. Sen. Sec. Public School Submitted By : Charchit Bansal Submitted To : Ms. Shikha mam Class : 8 th C Roll No. : 4 Admn. No. : 7026 Subject : Mathematics SUNAM
1. Submitted By : Charchit Bansal Submitted To : Ms. Shikha mam
Class : 8th C Roll No. : 4 Admn. No. : 7026
2. 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. Introduction
3. In general, if natural number m can be expressed as n2 ,
when n is also a natural number, then m is a square number. Example
52 = 25 62 = 36 The numbers 1,4,9,16are square numbers. These are
also called perfect squares.
4. Properties of square numbers Property 1- A number having
2,3,7or8 at units place is never a perfect square. Eg: Numbers 152,
7693, 1437, 88888 arent 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.
5. Property 4- If a number has 1 or 9 in its ones place, its
square will end in 1. Eg: 12=1, 92=81
6. 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 .
7. Finding square root of a perfect 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.
8. 1. THE METHOD OF REPEATED SUBTRACTION 2. PRIME FACTORIZATION
METHOD 3. LONG DIVISION METHOD Methods to find Square Root
9. 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.
10. 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
square root.
11. Step1- Obtain the number whose square root is to be
competed. 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 first period.
12. 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 number.