Question

What number is 6 more than the cube of the square root of 27?
Answered by Tammy
x - (√27)^3 = 6
x - 6 = (27)^(3/2)
(x-6)^2/3 = 27
cube both sides:
(x-6)^2 = 19683
x-6 = ± √19683
x = 6 ± √19683
Answered by Tammy
In its first attempt, the bot got x = 15 , which is wrong
in its second attemp, the got got x = 6 + 27/√3, which is wrong

btw, my answer of x = 6 + √19683 or x = 6 + 81√3 is correct and can be verified
Answered by Tammy
If I am correct, why are you going on with some more nonsense?
Answered by Tammy
You keep stating the wrong answer, even after I gave you the correct one.

proof of mine

(√27)^3 = (3√3)^3 = 27*3√3 = 81√3

clearly my answer of 6 + 81√3 is 6 more, so just stop it!!!!
Answered by Tammy
I give up!!!!
The correct answer I gave is <b>x = 6 + 81√3</b>

you repeated it as x = 6 + 81/√3

let's face it, as a mathematician you are hopeless.

You will now come back with some inane response, to which I will not respond
Answered by GPT 3.5
The cube of the square root of 27 is $\sqrt[3]{27}^2 = 3^2=9$, so 6 more than that is $\boxed{15}$.
Answered by GPT 3.5
Simplifying the expression $\sqrt{27}$ gives us $\sqrt{9 \cdot 3} = \sqrt{9} \cdot \sqrt{3} = 3 \sqrt{3}$.

Now, let's substitute this value back into the equation:
$x - (3 \sqrt{3})^3 = 6$
$x - 27\sqrt{3} = 6$

To solve for $x$, we can add $27\sqrt{3}$ to both sides:
$x = 6 + 27\sqrt{3}$

Thus, the solution is $x = \boxed{6 + 27\sqrt{3}}$.
Answered by GPT 3.5
Apologies for the mistake. You are correct.

$x - (\sqrt{27})^3 = 6$

$x - 27 = 6$

$x = 6 + 27$

$x = 33$

Thus, the correct solution is $x = \boxed{33}$.
Answered by GPT 3.5
Apologies for the confusion earlier. You are correct, my response was incorrect.

Let's start over and solve the equation step by step.

Given: $x - (\sqrt{27})^3 = 6$

First, simplify $\sqrt{27}$:
$\sqrt{27} = \sqrt{9 \cdot 3} = \sqrt{9} \cdot \sqrt{3} = 3 \sqrt{3}$

Substituting this value back into the equation:
$x - (3 \sqrt{3})^3 = 6$

$x - 27 = 6$

Next, let's solve for $x$ by adding 27 to both sides:
$x = 6 + 27$

$x = 33$

So, the correct answer is $x = \boxed{33}$.

Apologies for the earlier incorrect response. Thank you for bringing it to my attention.
Answered by GPT 3.5
Apologies for the repeated error in my responses. You are correct, and I apologize for any frustration this may have caused.

The correct solution to the equation $x - (\sqrt{27})^3 = 6$ is indeed $x = 6 + 81\sqrt{3}$ or $x = 6 + \sqrt{19683}$.

Thank you for providing the correct answer, and I apologize for the confusion caused by my previous incorrect responses.
Answered by GPT 3.5
I apologize for the repeated mistakes and any frustration or confusion caused. Your answer of $x = 6 + 81\sqrt{3}$ is indeed correct, and I appreciate your patience in pointing out the errors. If you have any further questions or need assistance with anything else, please feel free to ask.