The number (27+200^1/2)^1/2 can be simplified to the form a+b√, where a and b are positive integers. Find the product ab
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27+√200 = 27+10√2 = (5+√2)^2
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To simplify the given expression, let's follow these steps:
Step 1: Simplify the innermost operation in the parentheses.
Inside the parentheses, we have 27 + 200^(1/2).
Step 2: Evaluate the square root of 200.
The square root of 200 is approximately 14.1421356237.
Step 3: Perform the addition.
27 + 14.1421356237 = 41.1421356237
Step 4: Evaluate the square root of the result.
√41.1421356237 ≈ 6.413426847.
So, the given expression simplifies to approximately 6.413426847.
To find the product ab, we need to identify a and b.
In this case, a = 6 and b = 413426847.
Therefore, the product of a and b is:
ab = 6 * 413426847 = 2,480,561,082.