If $x^5 - 8 = 159$, what is the approximate value of $x$?
- $2.67$
- $2.71$
- $2.78$
- $2.81$
- $2.84$
Reveal answer
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C
Correct answer
Explanation
x^5 - 8 = 159 implies x^5 = 167. Taking the fifth root of 167, 2^5 = 32 and 3^5 = 243. Testing 2.78, 2.78^5 is approximately 166.5, which is very close to 167.
AI explanation
Adding 8 to both sides of the equation gives x raised to the power of 5 equals 167. Taking the fifth root of both sides shows that x equals the fifth root of 167. Since 2 raised to the power of 5 is 32 and 3 raised to the power of 5 is 243, x must be slightly less than 3. Checking the options by raising them to the fifth power, 2.78 multiplied by itself five times equals approximately 166.38, making it the closest value. The approximate value of x is 2.78.