nth Roots and Radicals
What is the value of the expression:
-root(3)(25^6)
-(25^2) = -625
((x^6y^3)/(x^(1/2)))^(2/3)
x^(11/3)y^2
What is the reduced radical form of the following expression:
root(4)(32) cdot root(4)(8)
4
Identify the domain and range for the function:
y=root(3)(2x-1)+1
The domain and range are both all real numbers
RR
sqrt(2x)=12
x=72
What is a potential solution that must be rejected?
An Extraneous Solution
2b^(-1/2)(-4b^(3/2)c^(1/5))^2
32b^(5/2)c^(2/5)
Rationalize the denominator:
1/(1-sqrt(5)
(1+sqrt(5))/-4
Identify the domain and range for the function:
y=sqrt(x+1)+3
Domain:
x geq -1
Range:
y geq 3
sqrt(25+x)+5=9
x=-9
Simplify the expression:
root(4)(81a^(28)b^(12)
3a^7b^3
((a^3b^6)/a^(1/3))^(4/3)
a^(32/9)b^8
Multiply:
root(3)(4)(10root(3)(2)-1)
20-root(3)(4)
Identify the function transformation(s):
y=4root(3)(2x)
Vertical stretch by 4 (multiply all y-values by 4)
Horizontal shrink by 2 (divide all x-values by 2)
x=1+sqrt(2x-2)
x=1 and x=3
Solve the equation:
750=6y^3
y=5
((m^(1/2)n^(-1/3))/(n^(2/3)m^(-7/4)))^(-1/6)
n^(1/6)/m^(3/8)
Multiply:
(sqrt(n)-sqrt(7))(sqrt(n)+5sqrt(7))
n-35+4sqrt(7n)
Where do the coordinates (0,0) and (1,1) get sent after completing the function transformation(s)?
y=-2sqrt(x-3)-pi
(0,0) to (3,-pi)
(1,1) to (4, -2-pi)
sqrt(6x-20)-x=-6
x=14
Rationalize the denominator:
1/root(3)(9x^4y^8
root(3)(3x^2y)/(3x^2y^3)
((q^3p^(-1/2))/(q^(-1/3)p))^(3/7)
q^(10/7)/p^(9/14)
Rationalize the denominator:
(4+sqrt(2))/(2-5sqrt(3))
(8+2sqrt(2)+20sqrt(3)+5sqrt(6))/-71
Identify the function transformation(s):
y=-1/2sqrt(2x-2)+4
Vertical Reflection
Vertical shrink by 1/2
Horizontal shrink by 2
Horizontal shift right 1
Vertical shift up 4
1+sqrt(1-x)=sqrt(x+4)
x=0