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square roots

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- 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 1,4,9,16………are square numbers. These are also called perfect squares.
- 4. 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.
- 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.

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