What is #x# in the equation #1000 = (x - 8) ^(3/2)#?

4 Answers
Aug 6, 2018

Answer:

#x=108#

Explanation:

#1000=(x-8)^(3/2)#

Cube root both sides

#10=(x-8)^(1/2)#

Square both sides

#100=x-8#

Add 8

#x=108#

Aug 6, 2018

Answer:

#x=108#

Explanation:

#(x-8)^(3/2)=1000#

#(x-8)^(3/2)=10^3#

#(x-8)^3=10^6#

#x-8=10^2#

#x=10^2+8=108#

Aug 6, 2018

Answer:

#x=108#

Explanation:

Note that #1000 = 10^3#

Raise both sides to the power of #2/3#

#(10^3)^(2/3) = ((x-8)^(3/2))^(2/3)#

Multiply the indices:

#10^2 =x-8#

#100 =x-8#

#108=x#

Aug 7, 2018

Answer:

#color(maroon)(x = 108#

Explanation:

#1000 = (x-8)^(3/2)#

#10^3 = (x - 8)^(3/2)#

#(100^(1/2))^3 = (x - 8)^(3/2)#

#100^(3/2) = (x - 8)^(3/2)#

#100 = x - 8#

#color(maroon)(x = 108#