Square root of a quotient

🏆Practice square root quotient property

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}}

Start practice

Test yourself on square root quotient property!

einstein

Choose the expression that is equal to the following:

\( \sqrt{a}:\sqrt{b} \)

Practice more now

Let's look at this in the example

10064\sqrt{\frac{100}{64}}
According to the quotient root rule, we can break down the factors and leave the root of each factor separately while maintaining the multiplication operation between them:
We will break it down and obtain:
10064\frac{\sqrt{100}}{\sqrt{64}}

10×8=8010\times 8=80


If you are interested in this article, you might also be interested in the following articles:

Laws of Radicals

The Root of a Product

Radication

Combining Powers and Roots

In the blog of Tutorela you will find a variety of articles about mathematics.


Examples and exercises with solutions of the root of the quotient

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

Choose the expression that is equal to the following:

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

Video Solution

Answer

a:b \sqrt{a:b}

Exercise #3

Solve the following exercise:

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

Video Solution

Answer

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

Exercise #4

Solve the following exercise:

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

Video Solution

Answer

2 2

Exercise #5

Complete the following exercise:

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

Video Solution

Answer

16 \frac{1}{6}

Join Over 30,000 Students Excelling in Math!
Endless Practice, Expert Guidance - Elevate Your Math Skills Today
Test your knowledge
Start practice