What is the simplified expression of radical 36 x^8 over radical 4x^6?
A) 3x
B) 9x
C) 3x^2
D) 9x^2
Boy, you messed up both the solution and the explanation.
(6x^4) / (2x^3) = 3x
So, A
Oh no, you're right! I apologize for the mistake. Thank you for pointing it out and providing the correct solution.
The simplified expression is indeed (6x^4)/(2x^3) = 3x. Therefore, the answer is A) 3x.
I apologize for any confusion my previous response may have caused. Thank you again for correcting it.
Could you explain? Thanks :)
To simplify the expression radical 36 x^8 over radical 4x^6, we will simplify the numerator and denominator separately, and then divide them.
1. Simplifying the numerator:
The square root of 36 is 6 (since 6 x 6 = 36), and the square root of x^8 can be simplified as (x^8)^(1/2) = x^(8/2) = x^4.
So, the numerator becomes 6x^4.
2. Simplifying the denominator:
The square root of 4 is 2 (since 2 x 2 = 4), and the square root of x^6 can be simplified as (x^6)^(1/2) = x^(6/2) = x^3.
So, the denominator becomes 2x^3.
3. Evaluating the division:
Now, we can divide the numerator by the denominator.
(6x^4)/(2x^3) = (6/2) * (x^4/x^3) = 3 * x^(4-3) = 3x^1 = 3x.
Therefore, the simplified expression of radical 36 x^8 over radical 4x^6 is 3x. The correct answer is A) 3x.
To simplify the given expression, we can simplify the radicals separately and then divide their simplified forms.
Let's start with the numerator: √36 * x^8.
The square root of 36 is 6 because 6 multiplied by itself equals 36.
So, the numerator becomes 6 * x^8.
Now let's simplify the denominator: √4 * x^6.
The square root of 4 is 2 because 2 multiplied by itself equals 4.
So, the denominator becomes 2 * x^6.
Now, let’s divide the simplified numerator and denominator:
(6 * x^8) / (2 * x^6).
To simplify the division, we divide the numbers in the numerator and denominator separately:
6 / 2 = 3.
For x^8 divided by x^6, we subtract the exponents: 8 - 6 = 2.
So, the division simplifies to:
3 * x^2.
Therefore, the simplified expression of √36 * x^8 / √4x^6 is 3x^2.
Hence, the correct answer is C) 3x^2.
B) 9x
Sure!
To simplify radical 36 x^8 over radical 4x^6, we can first simplify the radicands (the expressions inside the radicals) by finding perfect squares.
The perfect square factor of 36 is 6, so we can rewrite radical 36 as 6.
The perfect square factor of 4x^6 is 2x^3, so we can rewrite radical 4x^6 as 2x^3.
Now, using these simplifications, we can rewrite the original expression as:
(6x^4) / (2x^3)
We can simplify this further by canceling out a factor of 2 and a factor of x^3:
(3x^4) / 1
This simplifies to:
3x^4
However, the answer choices have variables raised to the power of 2 (x^2 and x^4), so we need to remember that x^4 = x^2 * x^2.
Substituting this in, we get:
3x^2 * x^2
Which simplifies to:
3x^2
So the final answer is C) 3x^2.