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

The value of $\sqrt{0.01}+\sqrt{0.81}+\sqrt{1.21}+\sqrt{0.0009}$ is:

Answer:

Explanation:

Given exp = $\sqrt{\frac{1}{100}}+\sqrt{\frac{81}{100}}+\sqrt{\frac{121}{100}}+\sqrt{\frac{9}{10000}}  =$

$\frac{1}{10}+\frac{9}{10}+\frac{11}{10}+\frac{3}{100}$

$0.1+0.9+1.1+0.03 = 2.13$

Find the value of $\sqrt{1\frac{9}{16} }$

Answer:

Explanation:

$\sqrt{1\frac{9}{16} } =  \sqrt{\frac{25}{16} } = \frac{\sqrt{25}}{\sqrt{16}}$
$=   1\frac{1}{4}$

If $\sqrt{.00000676} = .0026$, the square root of 67,60,000 is:

Answer:

Explanation:

$\sqrt{6760000} = \sqrt{0.00000676 \times 10^{12}}$
$=\sqrt{0.00000676} \times \sqrt{10^{12}}$
$= 0.0026 \times 10^{6}$
$= 2600.$

What is the square root of 0.16 ?  

Answer:

Explanation:

$\sqrt{16} = \sqrt{\frac{16}{100}}$
$= \frac{\sqrt{16}}{\sqrt{100}}$
$=\frac{4}{10}$
$= 0.4$

How many two-digit numbers satisfy this property : The last digit (unit's digit) of the square of the two-digit number is 8 ?

Answer:

Explanation:

A number ending in 8 can never be a perfect square.

• Square Roots and Cube Roots - General Questions