Answer:
Start with the expression: (sqrt(32) - sqrt(5))^(1/3) * (sqrt(32) + sqrt(5))^(1/3)
Notice that the terms inside the parentheses are conjugates of each other: sqrt(32) - sqrt(5) and sqrt(32) + sqrt(5).
When we multiply conjugates, the middle terms cancel out. So, we have: (sqrt(32))^2 - (sqrt(5))^2.
Simplifying further, we get: 32 - 5 = 27.
Now, we can rewrite the expression as: 27^(1/3).
The cube root of 27 is 3, so the final simplified expression is: 3.
Step-by-step explanation:
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Answer:
Start with the expression: (sqrt(32) - sqrt(5))^(1/3) * (sqrt(32) + sqrt(5))^(1/3)
Notice that the terms inside the parentheses are conjugates of each other: sqrt(32) - sqrt(5) and sqrt(32) + sqrt(5).
When we multiply conjugates, the middle terms cancel out. So, we have: (sqrt(32))^2 - (sqrt(5))^2.
Simplifying further, we get: 32 - 5 = 27.
Now, we can rewrite the expression as: 27^(1/3).
The cube root of 27 is 3, so the final simplified expression is: 3.
Step-by-step explanation: