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:

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

Suggested Topics to Practice in Advance

  1. Square root of a product

Practice Square Root Quotient Property

Examples with solutions for Square Root Quotient Property

Exercise #1

Solve the following exercise:

22525= \sqrt{\frac{225}{25}}=

Video Solution

Step-by-Step Solution

Let's simplify the expression. First, we'll reduce the fraction under the square root, then we'll calculate the result of the root:

22525=93 \sqrt{\frac{225}{25}}= \\ \sqrt{9}\\ \boxed{3} Therefore, the correct answer is option B.

Answer

3

Exercise #2

Solve the following exercise:

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

Video Solution

Answer

12 \frac{1}{\sqrt{2}}

Exercise #3

Solve the following exercise:

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

Video Solution

Answer

2 2

Exercise #4

Complete the following exercise:

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

Video Solution

Answer

16 \frac{1}{6}

Exercise #5

Choose the expression that is equal to the following:

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

Video Solution

Answer

a:b \sqrt{a:b}

Exercise #6

Solve the following exercise:

x4x= \frac{\sqrt{x^4}}{x}=

Video Solution

Answer

x x

Exercise #7

Solve the following exercise:

49x2x= \frac{\sqrt{49x^2}}{x}=

Video Solution

Answer

7 7

Exercise #8

Solve the following exercise:

25x2x2= \frac{\sqrt{25x^2}}{\sqrt{x^2}}=

Video Solution

Answer

5 5

Exercise #9

Solve the following exercise:

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

Video Solution

Answer

1 1

Exercise #10

Solve the following exercise:

14436= \sqrt{\frac{144}{36}}=

Video Solution

Answer

2 2

Exercise #11

Solve the following exercise:

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

Video Solution

Answer

4

Exercise #12

Solve the following exercise:

1444= \frac{\sqrt{144}}{\sqrt{4}}=

Video Solution

Answer

6 6

Exercise #13

Solve the following exercise:

102= \frac{\sqrt{10}}{\sqrt{2}}=

Video Solution

Answer

5 \sqrt{5}

Exercise #14

Solve the following exercise:

6416= \frac{\sqrt{64}}{\sqrt{16}}=

Video Solution

Answer

2

Exercise #15

Solve the following exercise:

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

Video Solution

Answer

4

Topics learned in later sections

  1. Square Roots
  2. Combining Powers and Roots
  3. Square Root Rules