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:

ab=ab\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:

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

Video Solution

Answer

a:b \sqrt{a:b}

Exercise #2

Solve the following exercise:

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

Video Solution

Answer

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

Exercise #3

Complete the following exercise:

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

Video Solution

Answer

16 \frac{1}{6}

Exercise #4

Solve the following exercise:

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

Video Solution

Answer

2 2

Exercise #5

Solve the following exercise:

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

Video Solution

Answer

3

Exercise #1

Complete the following exercise:

12111= \frac{\sqrt{121}}{11}=

Video Solution

Answer

1

Exercise #2

Complete the following exercise:

1964= \sqrt{\frac{196}{4}}=

Video Solution

Answer

7

Exercise #3

Complete the following exercise:

19649= \sqrt{\frac{196}{49}}=

Video Solution

Answer

2

Exercise #4

Solve the following exercise:

1004= \sqrt{\frac{100}{4}}=

Video Solution

Answer

5

Exercise #5

Complete the following exercise:

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

Video Solution

Answer

3

Exercise #1

Complete the following exercise:

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

Video Solution

Answer

12 \frac{1}{2}

Exercise #2

Complete the following exercise:

10025= \sqrt{\frac{100}{25}}=

Video Solution

Answer

2

Exercise #3

Solve the following exercise:

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

Video Solution

Answer

4

Exercise #4

Solve the following exercise:

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

Video Solution

Answer

2

Exercise #5

Solve the following exercise:

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

Video Solution

Answer

4

Topics learned in later sections

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