what is cube root 3 + cube root 3
The correct answer and explanation is:
Correct Answer:
The cube root of 3 plus the cube root of 3 is: 33+33=233\sqrt[3]{3} + \sqrt[3]{3} = 2\sqrt[3]{3}
Explanation:
To solve this, begin by understanding what a cube root is. The cube root of a number is the value that, when multiplied by itself three times, gives the original number. In mathematical terms, if x=33x = \sqrt[3]{3}, then x3=3x^3 = 3. The cube root of 3 is an irrational number, approximately equal to 1.442.
Now consider this expression: 33+33\sqrt[3]{3} + \sqrt[3]{3}
Since both terms are the same, you are simply adding two identical values. This is similar to saying: x+x=2xx + x = 2x
In this case, x=33x = \sqrt[3]{3}, so the expression becomes: 2⋅332 \cdot \sqrt[3]{3}
This is called combining like terms. You cannot simplify the cube root of 3 further into a rational number, but you can express the sum by factoring out the common term.
This is different from adding square roots or cube roots of different numbers, which cannot be combined unless they simplify to like terms. For instance, 33+53\sqrt[3]{3} + \sqrt[3]{5} would stay in that form, because the terms are unlike and cannot be combined.
The concept of adding roots follows the same rules as adding variables or algebraic expressions. Only like terms can be added directly. Since both terms are cube root of 3, they are like terms and can be added easily.
So the final answer remains: 2332\sqrt[3]{3}
And this is the simplest and correct form of the expression.