**Simplifying Radical Expressions Involving Fractions Worksheet :**

Worksheet given in this section will be much useful for the students who would like to practice problems on simplifying radical expressions involving fractions.

Before look at the worksheet, if you would like to know, how to simplify radical expressions involving fractions,

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

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(2) | ||

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**Problem 1 :**

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

**Solution :**

√(5/16) = √5 / √16

√(5/16) = √5 / √(4 ⋅ 4)

Index of the given radical is 2.

Because its index is 2, we can take one term out of radical for every two same terms multiplied inside the radical sign.

√(5/16) = √5 / 4

**Problem 2 :**

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

**Solution :**

√(x^{4}/25) = √x^{4 }/ √25

√(x^{4}/25) = √(x^{2} ⋅ x^{2}) / √(5 ⋅ 5)

Index of the given radical is 2.

Because its index is 2, we can take one term out of radical for every two same terms multiplied inside the radical sign.

√(x^{4}/25) = x^{2 }/ 5

**Problem 3 :**

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

**Solution :**

^{3}√(4x^{2}/27) = ^{3}√4x^{2 }/ ^{3}√27

^{3}√(4x^{2}/27) = ^{3}√(4x^{2}) / ^{3}√(3 ⋅ 3 ⋅ 3)

Index of the given radical is 3.

Because its index is 3, we can one term out of radical for every three same terms multiplied inside the radical sign.

^{3}√(4x^{2}/27) = ^{3}√(4x^{2}) / 3

**Problem 4 :**

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

**Solution :**

^{4}√(5x^{3}/16) = ^{4}√(5x^{3}) / ^{4}√16

^{4}√(5x^{3}/16) = ^{4}√5x^{3 }/ ^{4}√(2 ⋅ 2 ⋅ 2 ⋅ 2)

Index of the given radical is 4.

Because its index is 4, we can take one term out of the radical for every four same terms multiplied inside the radical sign.

^{4}√(5x^{3}/16) = ^{4}√5x^{3 }/ 2

**Problem 5 :**

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

**Solution :**

^{4}√(3/81a^{8}) = ^{4}√3 / ^{4}√(81a^{8})

^{4}√(3/81a^{8}) = ^{4}√3 / ^{4}√(3a^{2 }⋅ 3a^{2} ⋅ 3a^{2} ⋅ 3a^{2})

Index of the given radical is 4.

Because its index is 4, we can take one term out of the radical for every four same terms multiplied inside the radical sign.

^{4}√(3/81a^{8}) = ^{4}√3 / 3a^{2}

**Problem 6 :**

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

**Solution :**

√(a^{6}/49) = √a^{6}/√49

√(a^{6}/49) = √(a^{3 }⋅ a^{3})/(7 ⋅ 7)

Index of the given radical is 2.

Because its index is 2, we can take one term out of the radical for every two same terms multiplied inside the radical sign.

√(a^{6}/49) = a^{3}/7

**Problem 7 :**

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

**Solution :**

√(5/9y^{4}) = √5 / √9y^{4}

√(5/9y^{4}) ^{ }= √5 / (3y^{2 }⋅ 3y^{2})

Index of the given radical is 2.

Because its index is 2, we can take one term out of the radical for every two same terms multiplied inside the radical sign.

√(5/9y^{4})^{ }= √5 / 3y^{2}

**Problem 8 :**

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

**Solution :**

^{3}√(7/8y^{6}) = ^{3}√7 / ^{3}√(8y^{6})

^{3}√(7/8y^{6}) = ^{3}√7 / ^{3}√(2y^{2}^{ }⋅ 2y^{2 }⋅ 2y^{2})

Index of the given radical is 3.

Because its index is 3, we can take one term out of the radical for every three same terms multiplied inside the radical sign.

^{3}√(7/8y^{6}) = ^{3}√7 / 2y^{2}

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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