# The root of a product - Examples, Exercises and Solutions

## The square root of a product

When we encounter a root that encompasses the entirety of the product, we can decompose the factors of the products and leave a separate root for each of them. Let's not forget to leave the multiplication sign between the factors we have extracted.

Let's put it this way:
$\sqrt{(a\cdot b)}=\sqrt{a}\cdot\sqrt{b}$

## Practice The root of a product

### Exercise #1

Look at the following rectangle:

ΔAEB is isosceles (AE=EB).

Calculate the perimeter of the rectangle ABCD.

### Step-by-Step Solution

$8+16\sqrt3$

### Exercise #2

Solve the following exercise:

$\sqrt{30}\cdot\sqrt{1}=$

### Video Solution

$\sqrt{30}$

### Exercise #3

Solve the following exercise:

$\sqrt{25x^4}=$

### Video Solution

$5x^2$

### Exercise #4

Solve the following exercise:

$\sqrt{1}\cdot\sqrt{25}=$

### Video Solution

$5$

### Exercise #5

Solve the following exercise:

$\sqrt{1}\cdot\sqrt{2}=$

### Video Solution

$\sqrt{2}$

### Exercise #1

Solve the following exercise:

$\sqrt{16}\cdot\sqrt{1}=$

### Video Solution

$4$

### Exercise #2

Choose the expression that is equal to the following:

$\sqrt{a}\cdot\sqrt{b}$

### Video Solution

$\sqrt{a\cdot b}$

### Exercise #3

Solve the following exercise:

$\sqrt{2}\cdot\sqrt{5}=$

### Video Solution

$\sqrt{10}$

### Exercise #4

Solve the following exercise:

$\sqrt{100x^2}=$

### Video Solution

$10x$

### Exercise #5

Solve the following exercise:

$\sqrt{16x^2}=$

### Video Solution

$4x$

### Exercise #1

Solve the following exercise:

$\sqrt{10}\cdot\sqrt{3}=$

### Video Solution

$\sqrt{30}$

### Exercise #2

Solve the following exercise:

$\sqrt{5}\cdot\sqrt{5}=$

### Video Solution

$5$

### Exercise #3

Solve the following exercise:

$\sqrt{25x^2}=$

### Video Solution

$5x$

### Exercise #4

Solve the following exercise:

$\sqrt{2}\cdot\sqrt{3}=$

### Video Solution

$\sqrt{6}$

### Exercise #5

Solve the following exercise:

$\sqrt{36x}=$

### Video Solution

$6\sqrt{x}$