In simple mathematical terms, the square of a number is a value that we acquire when the original number is multiplied by itself, whereas the square root of a number is the factor of that number which, when multiplied by itself, yields the actual number. For example- if x is the square root of y, then x*x=y, that is, x2=y, which helps us derive the formula-√y. We know, 9 is the perfect square of 3, which means 32=9, therefore, √9=3. The square root of every number is always positive which makes us conclude the fact that the original number can either be positive or negative. For example, both -3 and +3 are square roots of 9, although we find the positive numbers are mostly used.
Similarly, the cube of a number is a value that we obtain when the original number is multiplied thrice by itself, whereas the cube root of that number is the factor of the number which, when multiplied thrice by itself, produces the original number. For example- if a is the cube root of b, then, a*a*a=b, that is, a3=b, and the formula is 3√=b. Let’s take numbers to understand the concept better- 27 is the perfect cube of 3, so, 33=27, which means, 3√27=3.
Some important properties of the square root are as follows:
Let’s read about a few properties of a cube root as well:
There are different methods on how to find the square root of a number. Some of them are:
To learn more, visit the Cuemath website. A detailed explanation is given about square roots and cube roots.
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