Let's solve the equation [tex]\({x}^3 = 27\)[/tex].
1. Understand the Problem:
The problem is asking us to find a number [tex]\( x \)[/tex] such that when it is raised to the power of 3 (cubed), the result is 27.
2. Set Up the Equation:
The equation is:
[tex]\[
x^3 = 27
\][/tex]
3. Isolate [tex]\( x \)[/tex]:
To find [tex]\( x \)[/tex], we need to take the cube root of both sides of the equation. The cube root is the inverse operation of raising a number to the power of 3.
4. Apply the Cube Root:
Take the cube root of both sides:
[tex]\[
x = \sqrt[3]{27}
\][/tex]
5. Calculate the Cube Root:
We need to find the number which, when multiplied by itself three times, gives 27. In simpler terms, we are looking for a number [tex]\( x \)[/tex] such that:
[tex]\[
x \times x \times x = 27
\][/tex]
By considering perfect cubes, we know that:
[tex]\[
3 \times 3 \times 3 = 3^3 = 27
\][/tex]
Therefore:
[tex]\[
\sqrt[3]{27} = 3
\][/tex]
6. Conclusion:
Hence, the value of [tex]\( x \)[/tex] that satisfies the equation [tex]\( x^3 = 27 \)[/tex] is:
[tex]\[
x = 3
\][/tex]
So, the solution to the equation [tex]\({x}^3 = 27\)[/tex] is [tex]\(x = 3\)[/tex].
