# SIMPLIFYING RADICAL EXPRESSIONS INVOLVING FRACTIONS

Simplifying Radical Expressions Involving Fractions :

In this section, you will learn, how to simplify radical expressions involving fractions. Step 1 :

If you have radical sign for the entire fraction, you have to take radical sign separately got numerator and denominator.

Step 2 :

We have to simplify the radical term according to its power.

• If you have square root (√), you have to take one term out of the square root for every two same terms multiplied inside the radical.
• If you have cube root (3), we have to take one term out of cube root for every three same terms multiplied inside the radical.
• If you have fourth root (4), you have to take one term out of fourth root for every four same terms multiplied inside the radical.

Note :

In case, you have prime number in the denominator, we have to multiply both numerator and denominator by the prime number along with radical sign.

Step 3 :

After taking the terms out from radical sign, we have to simplify the fraction.

## Simplifying Radical Expressions Involving Fractions - Examples

Example 1 :

Use the quotient property to write the following radical expression in simplified form. Solution :

√(5/16)  =  √5/√16

=  √5/√(4 ⋅ 4)

Index of given radical term is 2. Since its index is 2, we can factor one term for every two same terms.

=  √5/4

Example 2 :

Use the quotient property to write the following radical expression in simplified form. Solution :

√(x4/25)  =  x4/√25

=  √(x2 ⋅ x2)/√(5 ⋅ 5)

Index of given radical term is 2. Since its index is 2, we can factor one term for every two same terms.

=  x2/5

Example 3 :

Use the quotient property to write the following radical expression in simplified form. Solution :

(4x2/27) =  ∛4x/√27

=  ∛(2x ⋅ 2x)/√(3 ⋅ 3 ⋅ 3)

Index of given radical term is 3. Since its index is 3, we can factor one term for every three same terms.

=  ∛4x2/3

Example 4 :

Use the quotient property to write the following radical expression in simplified form. Solution :

∜5x3/16  =  ∜5x16

=  ∜5x3/∜(2 ⋅ 2  ⋅ 2 ⋅ 2)

Index of given radical term is 4. Since its index is 4, we can factor one term for every four same terms.

=  ∜5x3/2

Example 5 :

Use the quotient property to write the following radical expression in simplified form. Solution :

∜3/81a8  =  ∜3 / 81a8

=  ∜3 / (3a⋅ 3a2 ⋅ 3a2 ⋅ 3a2)

Index of given radical term is 4. Since its index is 4, we can factor one term for every four same terms.

=  ∜3/3a2

Example 6 :

Use the quotient property to write the following radical expression in simplified form. Solution :

√a6/49  =  a6/49

√(a⋅ a3)/(7 ⋅ 7)

Index of given radical term is 2. Since its index is 2, we can factor one term for every two same terms.

=  a3/7

Example 7 :

Use the quotient property to write the following radical expression in simplified form. Solution :

√5/9y4  =  √5/9y4

√5/(3y⋅ 3y2)

Index of given radical term is 2. Since its index is 2, we can factor one term for every two same terms.

=  √5/3y2

Example 8 :

Use the quotient property to write the following radical expression in simplified form. Solution :

∛7/8y6  =  ∛7 / 8y6

=  ∛7/∛(2y2 ⋅ 2y⋅ 2y2)

Index of given radical term is 2. Since its index is 2, we can factor one term for every two same terms.

=  ∛7/2y2 After having gone through the stuff given above, we hope that the students would have understood, how to simplify radical expressions involving fractions.

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