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

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Answer 1 · 2015-11-09T16:32:10

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:

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

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