Radicals Quiz
Questions: 16 · 10 minutes
1. Which expression is equivalent to 1/(2 + √3) and has no radical in the denominator?
The sum 2 + √3
The quotient (2 − √3)/7
The difference 2 − √3
The difference √3 − 2
2. A square has an area of 40 square units. Between which consecutive whole numbers is its side length?
Between 19 and 20 units
Between 5 and 6 units
Between 7 and 8 units
Between 6 and 7 units
3. What is the real value of ∛(−64)?
Positive 4
Negative 4
Negative 8
No real value exists
4. For any real number a, what is the simplest form of ⁴√(16a⁴)?
Twice a, written as 2a
Twice the absolute value of a, written as 2|a|
Four times the absolute value of a, written as 4|a|
Twice the square of a, written as 2a²
5. Without using a calculator, which comparison correctly locates √30?
√30 is less than 5
√30 is exactly 6
√30 lies between 5 and 6
√30 lies between 6 and 7
6. A square has a side length of √(x + 1) units. If its side length is 5 units, what is x?
x equals 4
x equals 6
x equals 26
x equals 24
7. Which proposed value satisfies √(x + 6) = x?
Negative three
Positive three
Negative two
Positive six
8. What is the value of the conjugate product (√7 + 2)(√7 − 2)?
The whole number eleven
Seven minus four times √7
The irrational number √3
The whole number three
9. After rationalizing the denominator, what does 3 divided by √5 become?
The product 3√5
The quotient 3√5 divided by 5
The quotient √15 divided by 5
The rational number three-fifths
10. A student combines the like radicals 2√3 and 5√3. What is the correct sum?
7√3
7√6
10√3
7√9
11. Which expression is equivalent to √72 in simplest radical form?
3√8
8√2
6√2
12√6
12. Assume x is nonnegative. Which expression is equivalent to √(50x²)?
Five times x times √2
Twenty-five times x times √2
Ten times x times √5
Five times x squared times √2
13. For nonnegative x, which radical expression is equivalent to x raised to the three-halves power?
The product of x and its square root
The product of x cubed and its square root
The cube root of x squared
The square root of three times x
14. What is the simplified product √6 · √15?
3√10
3√5
9√10
√21
15. In the expression √19, what is the radicand?
The squared quantity, 19²
The radical symbol, √
The implied index, 2
The number under the radical, 19
16. For which real values of x is √(x − 5) defined?
All numbers less than or equal to 5
Only numbers strictly greater than 5
All numbers greater than or equal to 5
Every number on the real number line