Arithmetic aptitude :: Square Roots and Cube Roots :: General Questions

• Square Roots and Cube Roots - General Questions
• Square Roots and Cube Roots - Important Formulas and Facts

Square Root

If $x^{2} = y$, we say that the square root of y is x and we write, $\sqrt{y}=x$

Cube Root

The cube root of a given number x is the number whose cube is x. we denote the cube root of x = $\sqrt[3]{x}$

e.g. $\sqrt[3]{27} = \sqrt[3]{3\times3\times3} = 3$

Note:

1)$\sqrt{xy}=\sqrt{x}\times\sqrt{y}$
2)$\sqrt{\frac{x}{y}}=\frac{\sqrt{x}}{\sqrt{y}}=\frac{\sqrt{x}}{\sqrt{y}}\times\frac{\sqrt{y}}{\sqrt{y}}=\frac{\sqrt{xy}}{y}$

$\sqrt{110 \frac{1}{4} } = ?$

Answer:

Explanation:

$\sqrt{  100 \frac{1}{4}} =  \sqrt{  \frac{441}{4}}$
$= \frac{\sqrt{441}}{\sqrt{4}}$
$=\frac{21}{2}$
$=10.5$

If y = 5, then what is the value of $10y\sqrt{  y^{3}-y^{2} }?$

Answer:

Explanation:

$10y\sqrt{  y^{3}-y^{2} } = 10 \times 5 \sqrt{  5^{3}-5^{2} } $
$=50 \times \sqrt{  125- 25}$
$= 50 \times \sqrt{  100}$
 
$= 50 \times 10 = 500$

If $x \times y = x + y + \sqrt{xy}$, the value of $6 \times 24$ is :

Answer:

Explanation:

$6 \times 24 = 6 + 24 +  \sqrt{6 \times 4}$

$= 30 + \sqrt{144} = 30 + 12 = 42.$

$\left( \sqrt{\frac{225}{729} }  - \sqrt{\frac{25}{144} } \right) + \sqrt{\frac{16}{81} }  = ?$

Answer:

Explanation:

Given exp = $\sqrt{\frac{225}{729} }  - \sqrt{\frac{25}{144} } - \sqrt{\frac{16}{81} }$
$= ( \frac{15}{27} - \frac{5}{12} ) +    \frac{4}{9}$
$= (\frac{15}{108} \times \frac{9}{4}  )$
$= \frac{5}{16}$

$\frac{\sqrt{625}}{11} \times \frac{14}{\sqrt{25}} \times \frac{11}{\sqrt{196}}$

Answer:

Explanation:

$\frac{25}{11} \times \frac{14}{5}   \times \frac{11}{14} =5.$

• Square Roots and Cube Roots - General Questions