Simplify the radical expression.
√20x^13y^5/ 5xy^7
A. 4x^12/y^2
B. 2x^6/y
C. 2√x^12/y^2
D. 2x^6y ***
No,
Assuming you meant:
√ (20x^13y^5/ (5xy^7) )
= √(4 x^12 / y^2 )
= 2x^6 / y , which would be B.
Ah okay. Must've had a few typos right there. Thank you =)
To simplify the radical expression √(20x^13y^5)/(5xy^7), we can start by simplifying the expression within the radical and then simplifying the expression outside the radical.
First, let's simplify the expression within the radical, √(20x^13y^5)/(5xy^7):
Using the properties of radicals, we can rewrite the expression as:
√(20x^13y^5)/(5xy^7) = √(20 * x^13 * y^5) / (5 * x * y^7)
Next, let's simplify the expression inside the radical:
√(20 * x^13 * y^5) = √(4 * 5 * x^12 * x * y^4 * y) = 2x^6y * √5xy
Finally, let's simplify the expression outside the radical:
2x^6y * √5xy / (5 * x * y^7) = (2x^6y / (5 * x * y^7)) * √(5xy)
= (2/5) * (x^6 / x) * (y / y^7) * √(5xy)
= (2/5) * x^5 * (1/y^6) * √(5xy)
So the simplified expression is: (2/5) * x^5 * (1/y^6) * √(5xy), which is equivalent to option D. 2x^6y.
To simplify the radical expression √20x^13y^5/ 5xy^7, we can follow these steps:
Step 1: Simplify the terms inside the radical:
The square root of 20 can be simplified as follows:
√20 = √(4 * 5) = √4 * √5 = 2√5
Step 2: Simplify the variables in the numerator:
x^13 can be simplified as follows:
x^13 = x^12 * x = (x^6)^2 * x = x^6 * √x^2
Note: The square root of x^2 is equal to x.
Step 3: Simplify the variables in the denominator:
y^7 can be simplified as follows:
y^7 = y^5 * y^2 = y^5 * √y^2
Note: The square root of y^2 is equal to y.
Now, let's substitute these simplified terms back into the expression:
√20x^13y^5/ 5xy^7
= (2√5 * x^6 * √x^2 * y^5) / (5 * x * y)
= (2 * √5 * x^6 * x * y^5 * √x^2) / (5 * x * y)
Step 4: Cancel out common terms:
Cancel out x, y, and the square root of x^2:
= (2/5) * (x^6 * y^5 * √5 * √x^2)
= (2/5) * (x^6 * y^5 * √(5x^2))
Finally, we have the simplified radical expression:
√20x^13y^5/ 5xy^7 = (2/5) * (x^6 * y^5 * √(5x^2))
Therefore, the correct answer is C. 2√x^12/y^2.