**How to express mixed surd into pure surds :**

Here we are going to see how to express mixed surd into pure surds.

Pure surd stands for the radical term, which do not have any number in front of radical.

For example,

6√2 is not pure surd

√6 is pure surd

To convert the mixed surd into pure surd, we have to follow the steps given below.

The example given below will illustrate the method of expressing the mixed surds into pure surds.

**Example 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 = √(16^{2} ⋅ 2)

= √(256 ⋅ 2)

= √512

**Example 2 :**

Express the following mixed surd into pure surd

3^{3}√2

**Solution :**

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

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

3^{3}√2 = ^{3}√(3^{3} ⋅ 2)

= ^{ 3}√(3 ⋅ 3 ⋅ 3 ⋅ 2)

= ^{3}√54

**Example 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 2^{4}√5 as pure surd, we have to take power 4 for 2 and write it under radical sign.

2^{4}√5 = √(2^{4} ⋅ 5)

= √(16 ⋅ 5)

= √80

**Example 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 = √(6^{2} ⋅ 3)

= √(36 ⋅ 3)

= √108

**Example 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 = √(6^{2} ⋅ 5)

= √(36 ⋅ 5)

= √180

- 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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