**Simplify radical expressions with variables worksheet :**

Here we are going to see some practice questions on simplifying radical expressions with variables.

(1) Simplifying the following radical expressions | |

(2) Simplifying the following radical expressions | |

(3) Simplifying the following radical expressions | |

(4) Simplifying the following radical expressions |

**Question 1 :**

Simplifying the following radical expressions

**Solution :**

** = **√(2 x 2 x 2 x 2 x u x u x u x u x v x v x v)

Index of the given radical is 2.

Here we have four "2", four "u" and three "v". According to the index, we have to take two 2's, one u and one v instead of 2 same terms from the radical sign.

So we get

= 2 x 2 x u x u x v** **√v

= 4 u²v √v

Hence the answer is 4 u²v √v.

**Question 2 :**

Simplifying the following radical expressions

**Solution :**

** = **√(3 x 7 x 7 x m x m x m x n x n x n)

Index of the given radical is 2.

Number of "3" that we have = 1

Number of "7" that we have = 2

number of "m" that we have = 3 and

number of "n" that we have = 3

According to the index of the radical, we can take one term from the radical for every two same terms . So, we have to take one "7", one "m" and one "n" from the radical.

Hence the answer is 7mn √3mn

**Question 3:**

Simplifying the following radical expressions

**Solution :**

** = **√(3 x 5 x 5 x X x X x y)

Index of the given radical is 2.

Number of "3" that we have = 1

Number of "5" that we have = 2

number of "x" that we have = 2 and

number of "y" that we have = 1

According to the index of the radical, we can take one term from the radical for every two same terms. So, we have to take one "5", one "x" from the radical.

Hence the answer is 5x √3y

**Question 4 :**

Simplifying the following radical expressions

**Solution :**

** = 6 **√(2 x 6 x 6 x X x X)

Index of the given radical is 2.

Number of "2" that we have = 1

Number of "6" that we have = 2

number of "x" that we have = 2 and

According to the index of the radical, we can take one term from the radical for every two same terms. So, we have to take one "6", one "x" from the radical.

If we already have any number or variable out side radical sign, then we have to multiply those terms with the new terms.

= 6 (6x)√2 = 36 √2

Hence the answer is 36 √2.

After having gone through the stuff given above, we hope that the students would have understood "Simplify radical expressions with variables worksheet".

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