In this post, we shared the square root formula and cube root formula with examples. Before we go to the formulas, know what is square root and cube root.
Square root: a number which produces a specified quantity when multiplied by itself.
Cube root: the number which produces a given number when cubed.
1 . Square root Formula:
If x2 = y, we say that the square root of y is x and we write, √y = x.
Thus, √4 = 2, √9 = 3, √196 = 14.
2 . Cube Root Formula:
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
Square Root Example
Evaluate √6084 by factorization method .
Method: Express the given number as the product of prime factors.
Now, take the product of these prime factors choosing one out of every pair
of the same primes. This product gives the square root of the given number.
Thus, resolving 6084 into prime factors, we get:
6084 = 22 x 32 x 132
√6084 = (2 x 3 x 13) = 78.
Cube Root Example
Find the cube root of 2744.
Method: Resolve the given number as the product of prime factors and
take the product of prime factors, choosing one out of three of the same
prime factors. Resolving 2744 as the product of prime factors, we get:
2744 = 23 x 73.
3√2744= 2 x 7 = 14.
Download the Square root and Cube root Formulas in PDF