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

 

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