EXPRESS THE GIVEN SURD TO SIMPLEST FORM WORKSHEET

(1)  Express the following surd in its simplest form.

³√32

(2)  Express the following surd in its simplest form.

 √63

(3)  Express the following surd in its simplest form.

 √243

(4)  Express the following surd in its simplest form.

 ³√256

(5)  Express the following surd in its simplest form.

⁴√80

Answers

Question 1 :

Express the following surd in its simplest form.

³√32

Solution :

³√32  =  ³√(2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2)

Order of the given radical is 3.

So, we have to factor out one term for every three same terms.

  =  2 ³√(2 ⋅ 2)

  =  2 ³√4

Hence the simplified form of the given radical term  ³√32 is 2 ³√4.

Example 2 :

Express the following surd in its simplest form.

 √63

Solution :

√63  =  √(3 ⋅ 3 ⋅ 7)

Order of the given radical is 2.

So, we have to factor out one term for every two same terms.

  =  3 √7

Hence the simplified form of the given radical term √63 is 3√7.

Question 3 :

Express the following surd in its simplest form.

 √243

Solution :

√243  =  √(3 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3)

Order of the given radical is 2.

So, we have to factor out one term for every two same terms.

  =  (3 ⋅ 3) √3

=  9 √3

Hence the simplified form of the given radical term √243 is 9√3.

Question 4 :

Express the following surd in its simplest form.

 ³√256

Solution :

³√256  =  ³√(2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2)

Order of the given radical is 3.

So, we have to factor out one term for every three same terms.

  =  2 ⋅ 2 ⋅ 2 ⋅ 2

=  16

Hence the simplified form of the given radical term ³√256 is 16.

Question 5 :

Express the following surd in its simplest form.

⁴√80

Solution :

 ⁴√80  =   ⁴√(2 ⋅ 2 ⋅ 2  ⋅ 2 ⋅ 5) 

Order of the given radical is 4.

So, we have to factor out one term for every four same terms.

  =  2 ⁴√5

Hence the simplified form of the given radical term  ⁴√80 is 2 ⁴√5.

Related topics

• Rationalization of surds
• Comparison of surds
• Operations with radicals
• Ascending and descending  order of surds
• Simplifying radical expression
• Exponents and powers

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.