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 approximate value of $\frac{3\sqrt{12}}{2\sqrt{28}}+\frac{2\sqrt{21}}{\sqrt{98}}$ is :

Answer:

Explanation:

$\frac{3\sqrt{12}}{2\sqrt{28}}\times\frac{\sqrt{98}}{2\sqrt{21}}$
$=\frac{3\sqrt{3\times4}}{2\sqrt{7\times4}}\times\frac{\sqrt{49\times2}}{2\sqrt{21}}$
$=\frac{6\sqrt{3}}{4\sqrt{7}}\times\frac{7\sqrt{2}}{2\sqrt{21}}$
$=\frac{21\sqrt{6}}{4\sqrt{7\times21}}=\frac{21\sqrt{6}}{28\sqrt{3}}$
$=\frac{3}{4}\sqrt{2}=\frac{3}{4}\times1.414=3\times0.3535=1.0605$

Three- fifth of the square of a certain number is 126.15.What is the number?

Answer:

Explanation:

Let the number be x .then ,
$\frac{3}{5}x^{2}=126.15$
$=> x^{2}= (126.15 \times\frac{5}{3})-210.25$
$=> x=\sqrt{210.25}=14.5$

For what value of * the statement $(\frac{*}{15})(\frac{*}{135})$ =1 is true?

Answer:

Explanation:

Let missing number be x
then $x^{2}= 15\times135$
$=> x= \sqrt{15\times135}=\sqrt{15^{2}\times 3^{2}}=15\times3=45$

The digit in the unit's place in the square root of 15876 is :

Answer:

Explanation:

$15876 = 2^{2}\times 3^{2}\times 3^{2}\times 7^{2} =2\times3\times3\times7 =126$

By what least number 4320 be multiplied to obtain a number which is a perfect cube ?

Answer:

Explanation:

Clearly, $4320=2^{3}\times 3^{2}\times 2^{2}\times5$

to make perfect cube we need to add $2\times 5^{2}$

= 50

• Square Roots and Cube Roots - General Questions