1. 1. Submitted By : Charchit Bansal Submitted To : Ms. Shikha mam Class : 8th C Roll No. : 4 Admn. No. : 7026
2. 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. 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. 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. 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. 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. 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. 8. 1. THE METHOD OF REPEATED SUBTRACTION 2. PRIME FACTORIZATION METHOD 3. LONG DIVISION METHOD Methods to find Square Root
9. 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. 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. 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. 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.