EXPRESS MIXED SURD INTO PURE SURDS WORKSHEET

(1)  Express the following mixed surd into pure surd

16√2

(2)  Express the following mixed surd into pure surd

3³√2

(3)  Express the following mixed surd into pure surd

2 ⁴√5

(4)  Express the following mixed surd into pure surd

6 √3

(5)  Express the following mixed surd into pure surd

6 √5

Answers

Question 1 :

Express the following mixed surd into pure surd

16√2

Solution :

Here we have the number 16 in front of √2. The order the radical term is 2.

To express 16√2 as pure surd, we have to take square for 16 and write it under radical sign.

16√2  =  √(16² ⋅ 2)

  =   √(256 ⋅ 2)

  =   √512

Question 2 :

Express the following mixed surd into pure surd

3³√2

Solution :

Here we have the number 3 in front of √2. The order the radical term is 3.

To express 3³√2 as pure surd, we have to take cube for 3 and write it under radical sign.

3³√2  =  ³√(3³ ⋅ 2)

  =   ³√(3 ⋅ 3 ⋅ 3 ⋅ 2)

  =   ³√54

Question 3 :

Express the following mixed surd into pure surd

2 ⁴√5

Solution :

Here we have the number 2 in front of ⁴√5. The order the radical term is 4.

To express 2⁴√5 as pure surd, we have to take power 4 for 2 and write it under radical sign.

2⁴√5  =  √(2⁴ ⋅ 5)

=  √(16 ⋅ 5)

=  √80

Question 4 :

Express the following mixed surd into pure surd

6 √3

Solution :

Here we have the number 6 in front of 6 √3. The order the radical term is 2.

To express 6 √3 as pure surd, we have to take square for 6 and write it under radical sign.

6 √3  =  √(6² ⋅ 3)

=  √(36 ⋅ 3)

=  √108

Question 5 :

Express the following mixed surd into pure surd

6 √5

Solution :

Here we have the number 6 in front of 6 √5. The order the radical term is 2.

To express 6 √5 as pure surd, we have to take square for 6 and write it under radical sign.

6 √5  =  √(6² ⋅ 5)

=  √(36 ⋅ 5)

=  √180

Related topics

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

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