SOLUTION: change to simplest radical form: square root of (a + 3) divided by 2+ 3 times the square root of (a+3) √(a+3)÷2+3√(a+3)

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Question 534443: change to simplest radical form:
square root of (a + 3) divided by 2+ 3 times the square root of (a+3)
√(a+3)÷2+3√(a+3)
Answer by fcabanski(1391) About Me  (Show Source):
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(sqrt(a+3))/ (2+3(sqrt(a+3))) Remove the radical from the denominator by rationalizing the denominator.


Remember that (a+b)(a-b) = a^2 + b^2. We can remove a sqrt from the denominator a+sqrt by multiplying by a-sqrt. We can always multiply an expression by 1 without changing its value. 1 can be written as (a-sqrt)/(a-sqrt)


In this case multiply by (2-3(sqrt(a+3)))/(2-3(sqrt(a+3))).


((sqrt(a+3))/ (2+3(sqrt(a+3)))) * (2-3(sqrt(a+3))) =


(2sqrt(a+3) -3(a+3)) / (4 - 9(a+3))