Root of a quotient - Examples, Exercises and Solutions

Root of a quotient

When we find a root that is in the complete quotient (in the complete fraction), we can break down the factors of the quotient: the numerator and the denominator and leave the root separated for each of them. We will not forget to leave the division symbol: the dividing line between the factors we separate.

Let's put it this way:

$\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}$

Detailed explanation

Practice Root of a quotient

Question 1

Choose the expression that is equal to the following:

$\sqrt{a}:\sqrt{b}$

Question 2

Solve the following exercise:

$\sqrt{\frac{2}{4}}=$

Question 3

Solve the following exercise:

$\frac{\sqrt{36}}{\sqrt{9}}=$

Question 4

Complete the following exercise:

$\sqrt{\frac{1}{36}}=$

Question 5

Solve the following exercise:

$\sqrt{\frac{225}{25}}=$

examples with solutions for root of a quotient

Exercise #1

Choose the expression that is equal to the following:

$\sqrt{a}:\sqrt{b}$

Video Solution

Answer

$\sqrt{a:b}$

Exercise #2

Solve the following exercise:

$\sqrt{\frac{2}{4}}=$

Video Solution

Answer

$\frac{1}{\sqrt{2}}$

Exercise #3

Solve the following exercise:

$\frac{\sqrt{36}}{\sqrt{9}}=$

Video Solution

Answer

$2$

Exercise #4

Complete the following exercise:

$\sqrt{\frac{1}{36}}=$

Video Solution

Answer

$\frac{1}{6}$

Exercise #5

Solve the following exercise:

$\sqrt{\frac{225}{25}}=$

Video Solution

Answer

Question 1

Solve the following exercise:

$\frac{\sqrt{x^4}}{x}=$

Question 2

Solve the following exercise:

$\frac{\sqrt{49x^2}}{x}=$

Question 3

Solve the following exercise:

$\frac{\sqrt{25x^2}}{\sqrt{x^2}}=$

Question 4

Solve the following exercise:

$\frac{\sqrt{49}}{7}=$

Question 5

Solve the following exercise:

$\sqrt{\frac{144}{36}}=$