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.
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
Express the given surd to simplest form worksheet - Solution
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
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