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:
(ab)=ab\sqrt{(a\cdot b)}=\sqrt{a}\cdot\sqrt{b}

Practice The root of a product

Exercise #1

Look at the following rectangle:

AAABBBCCCDDDEEE84

ΔAEB is isosceles (AE=EB).

Calculate the perimeter of the rectangle ABCD.

Video Solution

Step-by-Step Solution

Answer

8+163 8+16\sqrt3

Exercise #2

Solve the following exercise:

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

Video Solution

Answer

30 \sqrt{30}

Exercise #3

Solve the following exercise:

25x4= \sqrt{25x^4}=

Video Solution

Answer

5x2 5x^2

Exercise #4

Solve the following exercise:

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

Video Solution

Answer

5 5

Exercise #5

Solve the following exercise:

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

Video Solution

Answer

2 \sqrt{2}

Exercise #1

Solve the following exercise:

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

Video Solution

Answer

4 4

Exercise #2

Choose the expression that is equal to the following:

ab \sqrt{a}\cdot\sqrt{b}

Video Solution

Answer

ab \sqrt{a\cdot b}

Exercise #3

Solve the following exercise:

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

Video Solution

Answer

10 \sqrt{10}

Exercise #4

Solve the following exercise:

100x2= \sqrt{100x^2}=

Video Solution

Answer

10x 10x

Exercise #5

Solve the following exercise:

16x2= \sqrt{16x^2}=

Video Solution

Answer

4x 4x

Exercise #1

Solve the following exercise:

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

Video Solution

Answer

30 \sqrt{30}

Exercise #2

Solve the following exercise:

55= \sqrt{5}\cdot\sqrt{5}=

Video Solution

Answer

5 5

Exercise #3

Solve the following exercise:

25x2= \sqrt{25x^2}=

Video Solution

Answer

5x 5x

Exercise #4

Solve the following exercise:

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

Video Solution

Answer

6 \sqrt{6}

Exercise #5

Solve the following exercise:

36x= \sqrt{36x}=

Video Solution

Answer

6x 6\sqrt{x}

Topics learned in later sections

  1. Square Roots
  2. Square Roots
  3. Square root of a quotient
  4. Combining Powers and Roots