If M = √4 + ∛4 + ∜4, then the value of M is:
A) less than 3
B) equal to 3
C) between 3 and 4
D) equal to 4
E) greater than 4
We are given that M = √4 + ^3√4 + ^4√4. We need to determine the approximate value of M.
Since √4 = 2, we need to determine the value of 2 + ^3√4 + ^4√4
Let's determine the approximate value of ^3√4. To find this value, we need to find the perfect cube roots just below and just above the cube root of 4.
^3√1 < ^3√4 < ^3√8
1 < ^3√4 < 2
Let's next determine the approximate value of ^4√4. To determine this value, we need to find the perfect fourth roots just below and just above the fourth root of 4.
^4√1 < ^4√4 < ^4√16
1 < ^4√4 < 2
Since both ^3√4 and ^4√4 are greater than 1, √4 + ^3√4 + ^4√4 > 2 + 1 + 1 = 4.
Answer:
E
Jeffrey Miller
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