5 CHAP - SQUARE ROOTS AND CUBE ROOTS IMPORTANT FACTS AND...

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SQUARE ROOTS AND CUBE ROOTS IMPORTANT FACTS AND FORMULAE Square Root: If x 2 = y, we say that the square root of y is x and we write, √y = x. Thus, √4 = 2, √9 = 3, √196 = 14. Cube Root: The cube root of a given number x is the number whose cube is x. We denote the cube root of x by 3 √x. Thus, 3 √8 = 3 √2 x 2 x 2 = 2, 3 √343 = 3 √7 x 7 x 7 = 7 etc. Note: 1.√xy = √x * √y 2. √(x/y) = √x / √y = (√x / √y) * (√y / √y) = √xy / y SOLVED EXAMPLES Ex. 1. Evaluate √6084 by factorization method . Sol. Method: Express the given number as the product of prime factors. 2 6084 Now, take the product of these prime factors choosing one out of 2 3042 every pair of the same primes. This product gives the square root 3 1521 of the given number. 3 507 Thus, resolving 6084 into prime factors, we get: 13 169 6084 = 2 2 x 3 2 x 13 2 13 6084 = (2 x 3 x 13) = 78. Ex. 2. Find the square root of 1471369. Sol. Explanation: In the given number, mark off the digits 1 1471369 (1213 in pairs starting from the unit's digit. Each pair and 1 the remaining one digit is called a period. 22 47 Now, 1 2 = 1. On subtracting, we get 0 as remainder. 44 Now, bring down the next period i.e., 47. 241 313 Now, trial divisor is 1 x 2 = 2 and trial dividend is 47. 241 So, we take 22 as divisor and put 2 as quotient. 2423 7269 The remainder is 3. 7269 Next, we bring down the next period which is 13. x Now, trial divisor is 12 x 2 = 24 and trial dividend is 313. So, we take 241 as dividend and 1 as quotient. The remainder is 72.
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This note was uploaded on 08/13/2011 for the course FSD 011 taught by Professor Vinh during the Spring '11 term at Beacon FL.

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5 CHAP - SQUARE ROOTS AND CUBE ROOTS IMPORTANT FACTS AND...

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