Square Root and Cube Root - Shortcuts and Formulas

Square Root and Cube Root Questions - Page 2
Square Root and Cube Root Video Lecture - Page 3

Square Root of a Number

The square root of a number is that number , the product of which by itself , is equal to the given number.

Important Example for Square Root and Cube Root

Example 1: The square root of x is denoted by $\sqrt{x}$

Thus $\sqrt{9}=3,\sqrt{25}=5,\sqrt{1000}=10$ etc.

Square Root of Factorization: When a given no is perfect square we resolve it in to prime factors and take the product of prime factors. choosing one out of every pair

Example 2: Given that $\sqrt{15}$ = 3.8729 evaluate $(\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}})$

Solution: $(\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}})$

= $(\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}})\times \frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}+\sqrt{3}}$

=$\frac{(\sqrt{5}+\sqrt{3})^{2}}{5-3}$ = $\frac{5+2+3\times \sqrt{5}\times \sqrt{3}}{2}$

$(4+\sqrt{15})$ = 4+3.8729 = 7.8729

Example 3: if $\sqrt{1369}$ = 37 find the value of $\sqrt{13.69}+\sqrt{.1369}+\sqrt{.001369}$

Solution: Given expression is , $\frac{\sqrt{1369}}{100}+\frac{\sqrt{1369}}{10000}+\frac{\sqrt{1369}}{100000}$

=$\frac{37}{10}+\frac{37}{100}+\frac{37}{1000}$ = 3.7+0.37+0.037 = 4.107

Cube Root of a Number: The cube root of a number x is the number whose cube is x . we denote cube root of x by $\sqrt[3]{x}$

Cube Root of Factorization: Resolve the given number in to prime factor and take the product of prime number .

thus $\sqrt[3]{343}\; =\; \sqrt[3]{7\times 7\times 7}$ =7