If the operator @ is defined as a@b = (ab)1/2Then what is (16@81)@49 =(A) 32(B) 42(C) 64(D) 80(E) None of the above
Question
If the operator @
is defined as a@b = (ab)^(1/2)
Then what is (16@81)@49
?
(A) 32
(B) 42
(C) 64
(D) 80
(E) None of the above
Solution
To solve this problem, we need to follow the operator @ definition which is a@b = (ab)^(1/2).
Step 1: First, we calculate the operation inside the parentheses, which is 16@81. According to the definition, this equals to (16*81)^(1/2).
Step 2: Multiply 16 and 81 to get 1296.
Step 3: Take the square root of 1296, which is 36.
Step 4: Now, we substitute 36 back into the original equation in place of 16@81, so we have 36@49.
Step 5: According to the definition of @, this equals to (36*49)^(1/2).
Step 6: Multiply 36 and 49 to get 1764.
Step 7: Take the square root of 1764, which is 42.
So, (16@81)@49 = 42. Therefore, the answer is (B) 42.
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