What is x if #x^(1/3)=3+sqrt(1/4)#?

1 Answer
Lotusbluete
Nov 9, 2015

First of all, you can simplify #sqrt(1/4)#:
#sqrt(1/4) = sqrt(1) / sqrt(4) = 1/2#

This means that # 3 + sqrt(1/4) = 3 + 1/2 = 7/2#.

Now, you have the following equation:

# x ^(1/3) = 7/2 <=> root(3)(x) = 7/2#

To solve this equation, you need to cube both sides:

# root(3)(x) = 7/2#
#<=> (root(3)(x))^3 = (7/2)^3#
# <=> x = (7/2)^3 = 7^3/2^3 = 343/8#.

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