Lesson Worksheet: nth Roots: Expressions and Equations Mathematics

In this worksheet, we will practice simplifying algebraic expressions and solving algebraic equations involving nth roots, where n is a positive integer greater than or equal to 2.

Q1:

Simplify: 64𝑚.

  • A16𝑚
  • B64𝑚
  • C4𝑚
  • D4𝑚
  • E16𝑚

Q2:

Simplify 100𝑥.

  • A100|𝑥|
  • B10𝑥
  • C100𝑥
  • D10|𝑥|
  • E10𝑥

Q3:

Write 25𝑎𝑏 in its simplest form.

  • A5𝑎𝑏
  • B||5𝑎𝑏||
  • C||25𝑎𝑏||
  • D||5𝑎𝑏||
  • E5𝑎𝑏

Q4:

Which of the following has the same value as 729𝑚𝑛?

  • Athe length of one side of a cube whose volume is 729𝑚𝑛
  • Bthe expression 243𝑚𝑛
  • Cthe length of one side of a square whose area is 729𝑚𝑛
  • Dthe expression 729𝑚𝑛

Q5:

Find the value (or values) of 𝑥 if 12𝑥=384.

Q6:

Simplify 512𝑥.

  • A4𝑥
  • B2𝑥
  • C2𝑥
  • D8𝑥
  • E64𝑥

Q7:

Find the solution set in for (2𝑥1)=64.

  • A𝜙
  • B{1.5,1.5}
  • C{0.5}
  • D{1.5,0.5}
  • E{1.5}

Q8:

Find the solution set in for (2𝑥+1)=81.

  • A{1}
  • B{1,1}
  • C𝜙
  • D{1,2}
  • E{2}

Q9:

Find the solution set in for 𝑥5=256.

  • A{3,3}
  • B{16,16}
  • C𝜙
  • D{1,3,1,3}
  • E{4,16,4,16}

Q10:

Find the value (or values) of 𝑥 given that 𝑥+95=144×3.

  • A𝑥=21
  • B𝑥=21 and 𝑥=39
  • C𝑥=21 and 𝑥=39
  • D𝑥=21 and 𝑥=39
  • E𝑥=39

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