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.
To simplify the expression (27+200^1/2)^1/2, we need to evaluate the innermost parenthesis first.
Calculating √200, which equals 14.1421356237 (approximated to several decimal places).
Then, we add 27 to 14.1421356237, which gives us 41.1421356237.
Next, we take the square root of 41.1421356237, which equals 6.415368.
Since the expression is already in simplified form, a is equal to 6 and b is equal to 415368.
Finally, we calculate the product ab: 6 * 415368 = 2,492,208.
Therefore, the product ab is 2,492,208.