# 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:

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

## Practice Root of a quotient

### Exercise #1

Choose the expression that is equal to the following:

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

### Video Solution

$\sqrt{a:b}$

### Exercise #2

Solve the following exercise:

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

### Video Solution

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

### Exercise #3

Complete the following exercise:

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

### Video Solution

$\frac{1}{6}$

### Exercise #4

Solve the following exercise:

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

### Video Solution

$2$

### Exercise #5

Solve the following exercise:

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

3

### Exercise #1

Complete the following exercise:

$\frac{\sqrt{121}}{11}=$

1

### Exercise #2

Complete the following exercise:

$\sqrt{\frac{196}{4}}=$

7

### Exercise #3

Complete the following exercise:

$\sqrt{\frac{196}{49}}=$

2

### Exercise #4

Solve the following exercise:

$\sqrt{\frac{100}{4}}=$

5

### Exercise #5

Complete the following exercise:

$\sqrt{\frac{81}{9}}=$

3

### Exercise #1

Complete the following exercise:

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

### Video Solution

$\frac{1}{2}$

### Exercise #2

Complete the following exercise:

$\sqrt{\frac{100}{25}}=$

2

### Exercise #3

Solve the following exercise:

$\sqrt{\frac{64}{4}}=$

4

### Exercise #4

Solve the following exercise:

$\frac{\sqrt{64}}{\sqrt{16}}=$

2

### Exercise #5

Solve the following exercise:

$\sqrt{\frac{64}{4}}=$