If 1 > x > 9/8, which is bigger, ∛3x or √2x.
3x
1 > x > 9/8
is not possible, since 1 < 9/8
To determine which is bigger between ∛3x and √2x, we need to compare their values.
Let's start by simplifying the expression 1 > x > 9/8. This means that x is greater than 9/8 and less than 1.
Now, let's consider ∛3x and √2x individually:
∛3x is the cube root of 3x.
√2x is the square root of 2x.
Since x is greater than 9/8 and less than 1, we know that x is a positive number. Therefore, we can compare ∛3x and √2x.
To compare these two expressions, we can analyze their exponents:
The exponent of ∛3x is 1/3 (because we are taking the cube root).
The exponent of √2x is 1/2 (because we are taking the square root).
When comparing exponents, a larger exponent means a higher power, resulting in a larger value.
Since 1/3 is greater than 1/2, we can conclude that ∛3x is larger than √2x.
In summary, if 1 > x > 9/8, then ∛3x is bigger than √2x.