Chapter 4: SQUARE AND CUBE ROOTS


Introduction


Squares and cubes of numbers up to 20:

Factorization method to get square root


To find the square root of a perfect square by using the prime factorization method when a given number is a perfect square:

Step I: Resolve the given number into prime factors.
Step II: Make pairs of similar factors.
Step III: Take the product of prime factors, choosing one factor out of every pair.

Q. Take square root of 484
484 = 2^2 * 11^2
So square root of 484 = square root
2^2 * 11^2 = 2*11 = 22

Q. Which number should be multiplied with 675 to get a perfect cube.
A.  675 = 5*5*3*3*3. Therefore another 5 needs to be multiplied to get perfect cube.

Q. 12+12+12+......  = ?
Assume the value be x.
12+12+12+......  = x
Squaring both sides,
12+12+12+12+...=x2
12+x=x2
x2x12=0 or (x-4) (x+3) = 0
or x = 4 as x can't be negative.

Q. if square root of 3 = 1.732 find square root of 192.

A. 192 = 3 * 2 * 2 * 2 * 2 * 2 * 2 so

square root of 192 = 8 * square root (3)


Quiz

Score more than 80% marks and move ahead else stay back and read again!