Question

On simplification \[{{x}^{3}}=27\], then x is equal to?

Answer 1

Hint: In this problem we have to solve and find the value of x. Here the given 27 is a perfect cubic number which was given in the square root and raised to the power 3. We can take cube root on both sides. We can then expand it as the cubic term and simplify it to get the final answer for x.

Complete step by step answer:
Here we have to find the value of x from the given equation
\[{{x}^{3}}=27\]
We can now take cube root on both the left-hand side and the right-hand side in the above step, we get
\[\Rightarrow \sqrt[3]{{{x}^{3}}}=\sqrt[3]{27}\]
We can now write the radical term above step as,
\[\Rightarrow {{x}^{3\times \dfrac{1}{3}}}=\sqrt[3]{27}\]
We can now cancel similar terms in the exponent of the left-hand sides, we get
\[\Rightarrow x=\sqrt[3]{27}\]
We know that 27 is a perfect cube, which can be written as 3 times of 3.
\[\Rightarrow x=\sqrt[3]{3\times 3\times 3}\]
We can now write the radical term in the above step as,
\[\Rightarrow x={{\left( 3 \right)}^{3\times \dfrac{1}{3}}}\]
We can now cancel the similar terms in the exponent of the left-hand side, we get
\[\Rightarrow x=3\]
Therefore, on solving the given equation, the value of x is 3.

Note: We should always remember some of the perfect cube terms to solve these types of problems. We should also remember that we can cube terms in the exponent and the radical symbol as the radical symbol indicates one third the power of the given term.