Free Compass Math Practice on Simplifying
Expressions with Radicals - Answers Included

A set of questions, with answers, on simplifying expressions with radicals, similar to the questions in the compass math test are presented. The answers to the questions are at the bottom of the page and the solutions with full explanations to these questions are also included.

  1. Simplify the expression with radicals given below

    2 √50 + 12 √8

    A) 14 √58
    B) 240
    C) 280
    D) 98
    E) 34 √2
  2. Simplify the expression given below

    √27 - √300

    A) √-273
    B) -7 √3
    C) -147
    D) 3 - 10√3
    E) 7√3
  3. Simplify the expression with radicals given below

    - 2 √(16y) + 10 √y

    A) 8 √y
    B) 8 √-(15y)
    C) 8 √(17y)
    D) 2 √(16y)
    E) 2 √y

  4. Simplify the expression given below

    2 √(x + 1) + 3 √(16x + 16)

    A) 14 √(x + 1)
    B) 5 √(17x + 17)
    C) 5
    D) √(17x + 17)
    E) 6 √(17x + 17)
  5. 2 √3 + 4 √12 + 3 √48 =

    A) 9 √3
    B) 9 √63
    C) 22
    D) 22 √3
    E) 9 √48
  6. Simplify the expression given below and rewrite it without radicals

    (√3 + √12) / (√3 - √12))

    A) 1
    B) 0
    C) -3
    D) - 1
    E) 3
  7. Simplify the expression with radicals given below

    5 √x + 6 √(9x) - 10 √(16x)

    A) √x
    B) -17 √x
    C) √(46 x)
    D) -2 √x
    E) √(-25 x)
  8. 2 √27 + 2 √75 =

    A) 16 √3
    B) 4 √3
    C) 4 √102
    D) 16
    E) 204
  9. √(103) + √(105) =

    A) √10,100
    B) 110 √10
    C) 10,000
    D) 2 √1000
    E) 2 √100,000
  10. Simplify the expression and rewrite it without radicals.

    √8 √3 √6

    A) 144
    B) 3
    C) 17
    D) 12
    E) 4

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