Use Property 2 to simplify each of the following radical expressions.
sqrt (10)/ sqrt(49)
My answer: sqrt (10) / (7)
THis next one i need help:
Use the properties for radicals to simplify each of the following expressions. Assume that
all variables represent positive real numbers.
sqrt ((12x ^3)/(5))
THis is what i have so far but i'm not sure :
(sqrt (4x^2 X 3x) X sqrt(5))/(sqrt(5))
i don't know what to do next...
right on one.
Second:
sqrt( (4x^2 X 3x)/ sqrt(5))
i don't know what to do next...
bring the 4x^2 out..
2x sqrt (3x/5)
first thing I would do would be to rationalize the denominator
sqrt((12x^3)/5)
(sqrt (60x^3))/5
then I would simplify the top
(2x(sqrt(15x)))/5
To simplify the expression sqrt(10)/sqrt(49), you can use Property 2 of radicals, which states that the square root of a product is equal to the product of the square roots. In this case, you can separate the numerator and denominator as follows:
sqrt(10) / sqrt(49) = sqrt(10) / (sqrt(7^2))
As 7 is a perfect square, you can take its square root:
= sqrt(10) / 7
So your answer, sqrt(10)/sqrt(49), simplifies to sqrt(10)/7.
Now, let's move on to the expression sqrt((12x^3)/5). To simplify this, we can use similar properties of radicals.
First, we separate the numerator and denominator as follows:
sqrt((12x^3)/5) = sqrt(4x^2 * 3x) / sqrt(5)
Next, we can simplify the numerator:
sqrt(4x^2 * 3x) = sqrt(4x^2) * sqrt(3x)
Taking the square root of 4x^2, we get 2x:
= 2x * sqrt(3x) / sqrt(5)
Finally, we can rationalize the denominator by multiplying both the numerator and denominator by sqrt(5):
= (2x * sqrt(3x) * sqrt(5)) / (sqrt(5) * sqrt(5))
Since the square root of 5 times the square root of 5 is simply 5, we can simplify further:
= (2x * sqrt(3x) * sqrt(5)) / 5
So your final answer for sqrt((12x^3)/5) is:
(2x * sqrt(3x) * sqrt(5)) / 5, or equivalently, (2x * sqrt(15x)) / 5.