Free Compass Math Practice Questions on Simplifying Expressions
with Radicals with Solutions and Explanations - Sample 8

Solutions with detailed explanations to compass math test practice questions in sample 8.

  1. Simplify the expression with radicals given below

    2 √50 + 12 √8

    Solution

    Use the fact that 50 = 2*25 and 8 = 2*4 to write

    2 √50 + 12 √8

    = 2 √(2*25) + 12 √(2*4)

    = 2 √2 √25 + 12 √2 √4

    Simplify

    = 2 * 5 * √2 + 12 * 2 * √2

    = 10 √2 + 24 √2 = 34 √2

  2. Simplify the expression given below

    √27 - √300

    Solution

    Use the fact that 27 = 3*9 and 8 = 3*100 to write

    √27 - √300

    = √(3*9) - √(3*100)

    = √3 √9 - √3 √100

    Simplify

    = 3 √3 - 10 √3 = - 7 √3

  3. Simplify the expression with radicals given below

    - 2 √(16y) + 10 √y

    Solution

    We first write

    - 2 √(16y) + 10 √y = - 2 √16 √y + 10 √y

    simplify

    = - 2 * 4 √y + 10 √y

    = -8 √y + 10 √y

    = 2 √y


  4. Simplify the expression given below

    2 √(x + 1) + 3 √(16x + 16)

    Solution

    We first factor (16x + 16) under the radical

    2 √(x + 1) + 3 √(16x + 16)

    = 2 √(x + 1) + 3 √[ 16(x + 1) ]

    = 2 √(x + 1) + 3 √16 √(x + 1)

    Simplify

    = 2 √(x + 1) + 3 * 4 * √(x + 1)

    = 2 √(x + 1) + 12 √(x + 1)

    = 14 √(x + 1)

  5. 2 √3 + 4 √12 + 3 √48 =

    Solution

    We first rewrite the given expression as

    2 √3 + 4 √12 + 3 √48

    = 2 √3 + 4 √(3*4) + 3 √(3*16)

    = 2 √3 + 4 √3 √4 + 3 √3 √16

    Simplify

    = 2 √3 + 8 √3 + 12 √3

    = 22 √3

  6. Simplify the expression given below and rewrite it without radicals

    (√3 + √12) / (√3 - √12)

    Solution

    We first rewrite the given expression as

    (√3 + √12) / (√3 - √12)

    = (√3 + √(3*4) / (√3 - √(3*4))

    Simplify

    = (√3 + 2 √3 / (√3 - 2 √3)

    = 3√3 / - √3

    = - 3

  7. Simplify the expression with radicals given below

    5 √x + 6 √(9x) - 10 √(16x)

    Solution

    We first rewrite the given expression as

    5 √x + 6 √(9x) - 10 √(16x)

    = 5 √x + 6 √9 √x - 10 √16 √x

    Simplify

    = 5 √x + 6*3 √x - 10*4 √x

    = 5 √x + 18 √x - 40 √x

    = -17 √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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