To solve the expression [tex]\(-2 \sqrt[3]{\frac{7}{8}}\)[/tex], follow these steps:
1. Understand the Expression:
- The expression involves the cube root of a fraction, [tex]\(\frac{7}{8}\)[/tex].
- After finding the cube root of this fraction, multiply the result by [tex]\(-2\)[/tex].
2. Compute the Cube Root of [tex]\(\frac{7}{8}\)[/tex]:
- Let's denote the cube root of [tex]\(\frac{7}{8}\)[/tex] as [tex]\( x \)[/tex]. So, [tex]\( x = \sqrt[3]{\frac{7}{8}} \)[/tex].
3. Cube Root Calculation:
- Find the cube root of the numerator [tex]\(7\)[/tex] and the denominator [tex]\(8\)[/tex].
- Cube root of 7 is approximately 1.913 as [tex]\(\sqrt[3]{7} ≈ 1.913\)[/tex].
- Cube root of 8 is 2 because [tex]\(2^3 = 8\)[/tex].
4. Form the Fraction:
- [tex]\( \sqrt[3]{\frac{7}{8}} \)[/tex] simplifies to [tex]\(\frac{\sqrt[3]{7}}{\sqrt[3]{8}} ≈ \frac{1.913}{2} \)[/tex].
5. Simplify the Result:
- [tex]\( \frac{1.913}{2} ≈ 0.9565 \)[/tex].
6. Multiply by [tex]\(-2\)[/tex]:
- Finally, multiply by [tex]\(-2\)[/tex]: [tex]\(-2 \times 0.9565 ≈ -1.913\)[/tex].
Thus, the value of [tex]\(-2 \sqrt[3]{\frac{7}{8}}\)[/tex] is approximately [tex]\(-1.9129311827723892\)[/tex].
So, [tex]\(-2 \sqrt[3]{\frac{7}{8}} ≈ -1.9129311827723892\)[/tex].
