Chapter 6 Mid Chapter TEST (6.1 – 6.3) REVIEW
Period _______ Name __________________________
1.
Find the real 4th root(s) of 256.
2. Find the real 6th root(s) of -729.
3. Find the real cubic root(s) of -125.
4. Find the real cubic root(s) of 343.
5
5. 162
Radical form:
Value:
6. 4096 4
Radical form:
Value (in fraction):
7.
Rational exponent form:
Value:
Rational exponent form:
Value:
Rational exponent form:
Value (round to 2 decimal places):
Rational exponent form:
value (round to 2 decimal places):
−3
6
√15625
5
8. ( √512)
3
9.
1
7
√5
10. ( √9)
4
−1
For 11 – 12, find the real solution(s) of the equation. Round to two decimal places if necessary.
11. 5𝑥 5 = −240
12. (𝑥 + 10)4 = 4096
13. What is the domain of a) the square root parent function? b) the cubic root parent function?
13. What is the domain and the range of y = 2√𝑥 + 2?
14. What is the domain and the range of y = −√𝑥 − 5?
15. List as many characteristics as you can of the parent cubic root function.
16. Let f(x) = √𝑥 . Transform the function
1) Translate 4 units to right.
3
2) Translate 4 units to left.
3) Reflect in the x-axis.
4) Reflect in the y-axis.
5) Vertically stretch by a factor of 4.
1
4
6) Vertically shrink by a factor of .
7) Horizontally stretch by a factor of 4.
1
4
8) Horizontally shrink by a factor of .
Write the expression in simplest form.
17. √432 =
3
18.
19.
20.
2
5+√3
√2
√5
=
omit this problem
=
4
√10
=
21. √54 + 2 √2 =
3
3
22. 2√75 − √3=
23. √250𝑥 10 =
(DO NOT ASSUME x is positive.)
3
24. √50𝑥 5 =
(DO NOT ASSUME x is positive.)
25. √8𝑥 3 − 𝑥√50𝑥
(Assume x is positive.)
26. √𝑥 4 𝑦 8 𝑧10
(DO NOT ASSUME all variables are positive.)
4