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Quantitative Aptitude :: Square Root and Cube Root

Square Root and Cube Root Important Formulas


1. Square Root:

If x2 = y, we say that the square root of y is x and we write \(\sqrt{y}\) = x.

Thus, \(\sqrt{4}\) = 2, \(\sqrt{9}\) = 3, \(\sqrt{144}\) = 12.


2. 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 \(\sqrt[3]{x}\).

Thus, \(\sqrt[3]{27}\) = 3 x 3 x 3 = 3, \(\sqrt[3]{343}\) = 7 x 7 x 7 = 7 etc.


Note:


1. \(\sqrt{xy}\) = \(\sqrt{x}\) x \(\sqrt{y}\)

2. \(\sqrt{\frac{x}{y}}\) = \(\frac{\sqrt{x}}{\sqrt{y}}\) = \(\frac{\sqrt{x}}{\sqrt{y}}\) x \(\frac{\sqrt{y}}{\sqrt{y}}\) = \(\frac{\sqrt{xy}}{y}\)