Question

How do you solve \[{{x}^{3}}+27=0\] ?

Answer 1

Hint: In this problem, we have to solve and find the value of x. We know that we can write the number 27 in cubic form as the number 27 is a perfect cube. We can first subtract 27 on both the sides in the given equation and cancel similar terms on the left-hand side, then we can take the cubic root on both sides. We can convert the cubic root into fraction exponent in order to cancel the power terms to solve and get the value of x.

Complete step by step answer:
We know that the given cubic equation to be solved is,
\[{{x}^{3}}+27=0\]
Now we can subtract the number 27 on both sides, we get
\[\Rightarrow {{x}^{3}}+27-27=0-27\]
Now we can cancel the similar terms with opposite sign, we get
\[\Rightarrow {{x}^{3}}=-27\]
Now we can take cubic root on both the sides, we get
\[\Rightarrow \sqrt[3]{{{x}^{3}}}=\sqrt[3]{-27}\]
We can write the number 27 as 3 cubes as it is a perfect cube.
We can now convert the cubic root into a fraction exponent to cancel the cubic root, we get
\[\Rightarrow {{x}^{3\times \dfrac{1}{3}}}=-{{3}^{3\times \dfrac{1}{3}}}\]
Now we can cancel the similar terms in the power, we get
\[\Rightarrow x=-3\]

Therefore, the value of x is -3.

Note: Students may get confused in taking the cubic root for negative terms, if the number inside the cubic root is a perfect square, it can be easily written in its cubic form irrespective of the sign. We should also know to convert a cubic root into a fractional exponent form.