Simplify the radical expression
square root of 56x^2
@Bot
Answer Choices
28x
2x sq root 14
2x sq root 7
2 sq root 14x^2
13 answers
2x square root(14)
Simplify 4sq root 6 over sq root of 30 by rationalizing the denominator. Show your work
We can simplify by rationalizing the denominator in the following way:
(4 square root(6))/(square root(30)) * (square root(30))/(square root(30))
= (4 square root(6) square root(30))/(30)
= (4 square root(180))/(30)
= (4 square root(36*5))/(30)
= (4 * 6 square root(5))/(30)
= (24 square root(5))/(30)
= (12 square root(5))/(15)
= 4/5 * square root(5)
Therefore, (4 square root(6))/(square root(30)) = 4/5 * square root(5).
(4 square root(6))/(square root(30)) * (square root(30))/(square root(30))
= (4 square root(6) square root(30))/(30)
= (4 square root(180))/(30)
= (4 square root(36*5))/(30)
= (4 * 6 square root(5))/(30)
= (24 square root(5))/(30)
= (12 square root(5))/(15)
= 4/5 * square root(5)
Therefore, (4 square root(6))/(square root(30)) = 4/5 * square root(5).
Simplify the radical expression
sq root 150 x^3 k^4
sq root 150 x^3 k^4
To simplify, we need to break down 150, x^3 and k^4 into their prime factors:
150 = 2 * 3 * 5^2
x^3 = x^2 * x
k^4 = (k^2)^2
Now we can simplify the original expression as follows:
square root(150 x^3 k^4)
= square root(2 * 3 * 5^2 * x^2 * x * k^2 * k^2)
= square root(2 * 3 * 5^2) * square root(x^2) * square root(x) * square root(k^2) * square root(k^2)
= 5xk^2 * square root(6x)
Therefore, the simplified radical expression is 5xk^2 * square root(6x).
150 = 2 * 3 * 5^2
x^3 = x^2 * x
k^4 = (k^2)^2
Now we can simplify the original expression as follows:
square root(150 x^3 k^4)
= square root(2 * 3 * 5^2 * x^2 * x * k^2 * k^2)
= square root(2 * 3 * 5^2) * square root(x^2) * square root(x) * square root(k^2) * square root(k^2)
= 5xk^2 * square root(6x)
Therefore, the simplified radical expression is 5xk^2 * square root(6x).
Simplify the radical expression
sq root 14q x 2 sq root 4q
sq root 14q x 2 sq root 4q
We can simplify this expression as follows:
square root(14q) * 2 square root(4q)
= square root(2 * 7 * q) * 2 * square root(2 * 2 * q)
= (square root(2) * square root(7) * square root(q)) * 2 * (2 * square root(q))
= (2 * square root(2) * square root(7) * square root(q)) * (2 * square root(q))
= 4 * 2 * square root(2 * 7) * square root(q) * square root(q)
= 8q * square root(14)
Therefore, the simplified radical expression is 8q * square root(14).
square root(14q) * 2 square root(4q)
= square root(2 * 7 * q) * 2 * square root(2 * 2 * q)
= (square root(2) * square root(7) * square root(q)) * 2 * (2 * square root(q))
= (2 * square root(2) * square root(7) * square root(q)) * (2 * square root(q))
= 4 * 2 * square root(2 * 7) * square root(q) * square root(q)
= 8q * square root(14)
Therefore, the simplified radical expression is 8q * square root(14).
Sorry but the answer choices are:
3 sq root of 56q^2
4q sq root 14
2 sq root of 56q^2
4 sq root of 14q^2
3 sq root of 56q^2
4q sq root 14
2 sq root of 56q^2
4 sq root of 14q^2
No problem. Here's how to get to the correct answer:
square root(14q) * 2 square root(4q)
= square root(14q) * 2 * 2 square root(q) (since 4q = 2*2*q)
= 2 * square root(14q) * 2 square root(q)
= 4 square root(14q^2)
= 4q square root(14)
Therefore, the simplified radical expression is 4q square root(14), which matches with the second answer choice.
square root(14q) * 2 square root(4q)
= square root(14q) * 2 * 2 square root(q) (since 4q = 2*2*q)
= 2 * square root(14q) * 2 square root(q)
= 4 square root(14q^2)
= 4q square root(14)
Therefore, the simplified radical expression is 4q square root(14), which matches with the second answer choice.
Simplify the radical expression
sq root 20x^13 y^5 over 5xy^7
sq root 20x^13 y^5 over 5xy^7
We can simplify this expression by breaking down the numerator into its prime factors:
sqrt(20x^13 y^5) = sqrt(2*2*5*x^12*x*y^4*y)
Then, we can simplify the expression as follows:
sqrt(20x^13 y^5) / (5xy^7)
= (sqrt(2*2*5*x^12*x*y^4*y)) / (5xy^7)
= (2x^6 y^2 * sqrt(5x)) / (5xy^7)
= (2x^5 * sqrt(5x)) / (5y^5)
Therefore, the simplified radical expression is (2x^5 * sqrt(5x)) / (5y^5).
sqrt(20x^13 y^5) = sqrt(2*2*5*x^12*x*y^4*y)
Then, we can simplify the expression as follows:
sqrt(20x^13 y^5) / (5xy^7)
= (sqrt(2*2*5*x^12*x*y^4*y)) / (5xy^7)
= (2x^6 y^2 * sqrt(5x)) / (5xy^7)
= (2x^5 * sqrt(5x)) / (5y^5)
Therefore, the simplified radical expression is (2x^5 * sqrt(5x)) / (5y^5).
Sorry but the answer choices are
sq root 4x^12 over y^2
2x^6 over y
2 sq root x^12 over y^2
2x^6y
sq root 4x^12 over y^2
2x^6 over y
2 sq root x^12 over y^2
2x^6y
No problem. Let's see how we can simplify the expression to match one of the answer choices.
sqrt(20x^13 y^5) / (5xy^7)
= sqrt(4 * 5 * x^12 * x * y^4 * y) / (5xy^7)
= (2x^6y^2 * sqrt(5x)) / (5xy^7)
= (2x^6 * sqrt(5x)) / (5y^5)
This simplifies to the third answer choice: 2 sqrt(x^12) / y^2.
So, the simplified radical expression is 2 sqrt(x^12) / y^2.
sqrt(20x^13 y^5) / (5xy^7)
= sqrt(4 * 5 * x^12 * x * y^4 * y) / (5xy^7)
= (2x^6y^2 * sqrt(5x)) / (5xy^7)
= (2x^6 * sqrt(5x)) / (5y^5)
This simplifies to the third answer choice: 2 sqrt(x^12) / y^2.
So, the simplified radical expression is 2 sqrt(x^12) / y^2.
1 answer