{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

5 CHAP

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

This preview shows pages 1–2. Sign up to view the full content.

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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 5

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online