simplify the following radical expression; 4 sqrt (81/16)
a) 2/3
b) 2
c) 3
d) 3/2
Assume you mean
(81/16)^(1/4)
(3*3*3*3/2*2*2*2)^(1/4) = 3/2
To simplify the radical expression 4 sqrt (81/16), we can simplify the numerator and the denominator separately, and then simplify the square root.
First, simplify the numerator:
81 can be written as 9^2.
16 can be written as 4^2.
So, 81/16 can be simplified to (9^2)/(4^2).
Next, simplify the square root:
√(9^2)/(4^2) = (9/4).
Finally, multiply the coefficient 4 with the simplified square root:
4 * (9/4) = 9.
Therefore, the simplified radical expression is 9.
The answer is not among the options given.
To simplify the expression 4 sqrt (81/16), we can start by simplifying the square root part.
First, let's simplify the radicand (the expression inside the square root). We have 81/16.
To simplify this, we can find the square root of both the numerator and the denominator separately.
The square root of 81 is 9, and the square root of 16 is 4.
So, we have 4 sqrt (9/4) remaining.
Next, we can simplify the fraction inside the square root.
We can divide both the numerator and the denominator by their greatest common divisor, which is 1.
Dividing 9 by 1 gives us 9, and dividing 4 by 1 gives us 4.
So, we have 4 sqrt (9/4) = 4 sqrt (9)/sqrt (4) = 4*3/2 = 12/2 = 6.
Therefore, the simplified radical expression 4 sqrt (81/16) is equal to 6.
So, the correct answer is c) 3.