Radical Expressions Quiz

Grade 9 · Math · Quiz

Challenge yourself on simplifying, combining, multiplying, and rationalizing radical expressions.

Questions

1. Simplify √75.

   1. 5√3
   2. 3√5
   3. 25√3
   4. 15√5
   Show answer

   Answer: 5√3

   Factor 75 = 25 · 3. √(25 · 3) = 5√3.

2. Simplify: 2√18 − √8

   1. √10
   2. 4√2
   3. 2√10
   4. 10√2
   Show answer

   Answer: 4√2

   2√18 = 2·3√2 = 6√2. √8 = 2√2. So 6√2 − 2√2 = 4√2.

3. Multiply: (√6)(√24)

   1. √30
   2. 12
   3. 6√4
   4. 4√6
   Show answer

   Answer: 12

   √6 · √24 = √(6 · 24) = √144 = 12.

4. Rationalize the denominator of 4/(√2 + √3).

   1. 4(√3 − √2)
   2. 4(√2 + √3)
   3. 4(√3 + √2)/5
   4. 4(√3 − √2)/1
   Show answer

   Answer: 4(√3 − √2)/1

   Multiply by the conjugate (√3 − √2): 4(√3 − √2)/((√3)² − (√2)²) = 4(√3 − √2)/(3 − 2) = 4(√3 − √2)/1.

5. Simplify (3√2)².

   1. 6
   2. 9√2
   3. 18
   4. 6√2
   Show answer

   Answer: 18

   (3√2)² = 3² · (√2)² = 9 · 2 = 18.

6. Which expression is equivalent to √(x⁴y²) for x ≥ 0, y ≥ 0?

   1. x²y
   2. xy²
   3. 2xy
   4. x⁴y²
   Show answer

   Answer: x²y

   √(x⁴y²) = √(x⁴) · √(y²) = x² · y = x²y.

7. √9 + √16 = √(9 + 16)

   Show answer

   Answer: False

   √9 + √16 = 3 + 4 = 7. But √25 = 5. Addition inside the radical is completely different from addition outside.

8. Multiply: (√5 + 2)(√5 − 2). The result is __.

   Show answer

   Answer: 1

   (√5 + 2)(√5 − 2) = (√5)² − 2² = 5 − 4 = 1. This is the difference of squares pattern.

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