What is the simpler form of the radical expression? 4sqrt 2401x^12y^16
I think the answer is either C or D.
A. 49|x^9|y^16
B. 49x^9|y^16|
C. 7|x^3|y^4
D. 7x^3|y^4|
What is the answer then!?
the answer should be
D. 7x^3|y^4|
Well, it seems like you're in the mood for some simplification, so let me clown around with those options for you!
Let's start by looking at the number 2401. It's a perfect square! You know what that means? It means we can take its square root and make it all nice and simple. So, the square root of 2401 is... drum roll, please... 49!
Now, let's focus on the x's and y's. We've got some exponents going on there. But fear not! We can simplify those too. Taking a closer look, we see that the x's have an exponent of 12 and the y's have an exponent of 16.
So here's the grand finale! After we've simplified everything, we end up with the answer: C. 7|x^3|y^4.
Why did I choose C instead of D, you may ask? Well, my funny friend, we're looking for the simpler form, and according to our clown math skills, C takes the cake! Or should I say, the clown pie? Mmm, pie...
To find the simplest form of the given radical expression, we need to simplify the expression inside the square root.
The square root of 2401 is 49 because the square root of a perfect square is the integer that was squared to get that perfect square.
Also, since x^12 = (x^6)^2 and y^16 = (y^8)^2, we can take the square root of x^12 and y^16 to simplify the expression further.
Therefore, the simplified form of the given expression is 4 * 49 * x^6 * y^8.
Now, let's look at the answer choices.
A. 49|x^9|y^16: This is not the simpler form since the exponent of x^6 is not reduced to the lowest possible value.
B. 49x^9|y^16|: This is not the simpler form since the exponent of x^6 is not reduced to the lowest possible value.
C. 7|x^3|y^4: This is the simpler form of the expression. The exponent of x has been reduced to the lowest possible value.
D. 7x^3|y^4|: This is not the simpler form since the exponent of y^8 is not reduced to the lowest possible value.
Therefore, the simpler form of the radical expression 4sqrt 2401x^12y^16 is C. 7|x^3|y^4.
as you typed it:
4√2401 x^12 y^16
= 4(49) x^12 y^16 , none of the choices
if you meant:
4√(2401 x^12 y^16)
= 4(49) x^6 y^8 , again none of the choices
if you meant:
(2401 x^12 y^16)^(1/4)
= 7 x^3 y^4 , then you shouldn't have used sqrt