
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
x2−x−12=0
or (x4) (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!