# EXPRESS THE GIVEN SURD TO SIMPLEST FORM WORKSHEET

## About "Express the given surd to simplest form worksheet"

Express the given surd to simplest form worksheet:

Here we are going to see some practice questions on express the given surd to simplest form.

## Express the given surd to simplest form worksheet - Practice questions

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

332

(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

## Express the given surd to simplest form worksheet - Solution

Question 1 :

Express the following surd in its simplest form.

332

Solution :

332  =  3√(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  332 is 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)

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 45

Hence the simplified form of the given radical term  4√80 is 45.

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