HOW TO EXPRESS A GIVEN SURD TO SIMPLEST FORM

Express the following surds in simplest form.

Example 1 :

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.

  =  2³√(2 ⋅ 2)

  =  2³√4

Example 2 :

 √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

Example 3 :

 √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

Example 4 :

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

Example 5 :

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.

  =  2⁴√5

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