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Worksheet: Radical Expressions to Exponential Expressions

Q1:

Express 1 1 √ π‘₯ 7 in the form π‘₯ 𝑛 .

  • A π‘₯ 1 4 1 1
  • B π‘₯ 1 1 7
  • C π‘₯ 1 1 1 4
  • D π‘₯ 7 1 1

Q2:

Express π‘₯ √ π‘₯ 5 2 3 2 4 in the form π‘₯ 𝑛 .

  • A π‘₯ 7 6
  • B π‘₯ 2 4 1 4 3
  • C π‘₯ 6 7
  • D π‘₯ 1 4 3 2 4

Q3:

What is ο€Ώ √ 1 0 √ 6  βˆ’ 2 ?

  • A √ 3 √ 5
  • B 9 2 5
  • C 5 3
  • D 3 5

Q4:

What is ο€Ώ √ 7 √ 1 4  βˆ’ 4 ?

  • A 2
  • B 16
  • C 1 4
  • D 4
  • E 1 2

Q5:

What is one-eighth of ο€» √ 8  7 1 4 ?

  • A 8 3
  • B 8 2
  • C 8 6
  • D8
  • E1

Q6:

Simplify 5 + ο€» √ 5  + ο€» √ 5  + ο€» √ 5  + ο€» √ 5  7 1 4 1 4 1 4 1 4 .

  • A 5 1 4
  • B 5 7
  • C 2 5 7
  • D 5 8
  • E 1 0 8

Q7:

Given that π‘Ž = √ 5 and 𝑏 = √ 2 , find the value of 𝑏 βˆ’ π‘Ž 𝑏 + π‘Ž 4 4 2 2 .

Q8:

Which of the following is equivalent to 3 √ 1 2 5 ?

  • A 1 2 5 3 1
  • B 3 1 2 5
  • C 1 2 5 1 2 5 1 3
  • D 1 2 5 1 3
  • E 1 2 5 Γ— 1 3

Q9:

Which of the following is equal to ο€Ώ βˆ’ √ 2 2  βˆ’ 2 ?

  • A 2 √ 2
  • B βˆ’ 2
  • C βˆ’ 2 √ 2
  • D 2
  • E 1 2

Q10:

What is the value of 4 + ο€Ώ βˆ’ 1 √ 4  + 1 √ βˆ’ 6 4 0 2 3 ?

  • A 4
  • B 1 4
  • C 16
  • D 1
  • E 8

Q11:

Which of the following is equal to 5 + ο€» √ 5  βˆ’ 5 ( 5 ) 6 1 2 6 ?

  • A βˆ’ 5 ( 5 ) 6
  • B βˆ’ 4 ( 5 ) 6
  • C ο€» √ 5  6
  • D βˆ’ 3 ( 5 ) 6
  • E 5 6

Q12:

Find the value of 5 ο„ž ο€» 1 βˆ’ √ 6  5 .

  • A ο€» 1 βˆ’ √ 6  5
  • B √ 6 βˆ’ 1
  • C 5  1 βˆ’ √ 6
  • D 1 βˆ’ √ 6

Q13:

Find the value of 3 6 ο„ž ο€» 2 9 βˆ’ √ 3  3 6 .

  • A ο€» 2 9 βˆ’ √ 3  3 6
  • B √ 3 βˆ’ 2 9
  • C 3 6  2 9 βˆ’ √ 3
  • D 2 9 βˆ’ √ 3

Q14:

Which of the following is equal to 1 6 √ π‘₯ 3 ?

  • A π‘₯ 1 6 3
  • B ο€½ π‘₯  1 3 1 6
  • C ο€Ί √ π‘₯  3 1 6
  • D ο€Ί √ π‘₯  1 6 3

Q15:

Which of the following is not equal to 1 3 √ π‘₯ 5 ?

  • A π‘₯ 5 1 3
  • B ο€½ π‘₯  1 1 3 5
  • C ο€Ί √ π‘₯  1 3 5
  • D ο€Ί √ π‘₯  5 1 3

Q16:

Which of the following is equal to 9 √ π‘₯ 4 ?

  • A π‘₯ 9 4
  • B ο€½ π‘₯  1 4 9
  • C ο€Ί √ π‘₯  4 9
  • D ο€Ί √ π‘₯  9 4

Q17:

Which of the following is equivalent to 3 √ 2 7 2 ?

  • A 2 7 3 2
  • B 2 7 2 7 2 3
  • C 2 7 2 7 2 1 3
  • D 2 7 2 3
  • E 3 2 2 7

Q18:

Which of the following denotes the 𝑛 t h root of π‘Ž ?

  • A βˆ’ π‘Ž 1 𝑛
  • B π‘Ž 1 2
  • C π‘Ž 1 3
  • D π‘Ž 1 𝑛