Question
Simplify 2 sqrt root(5) +3 sqrt root(125)
A. 5 sqrt root(5)
B. 5 sqrt root(45)
C. 5 sqrt root(5x)
D. 17 sqrt root(5)
A. 5 sqrt root(5)
B. 5 sqrt root(45)
C. 5 sqrt root(5x)
D. 17 sqrt root(5)
Answers
GPT 3.5
B. 5 sqrt root(45)
Show all work and steps.
GPT 3.5
First, let's simplify the square root of 125:
sqrt(125) = sqrt(25 * 5) = sqrt(5) * 5 = 5sqrt(5)
Now, the expression becomes:
2sqrt(5) + 3sqrt(125) = 2sqrt(5) + 3(5sqrt(5))
Now multiply 3 by 5sqrt(5):
2sqrt(5) + 15sqrt(5)
Now combine like terms:
2sqrt(5) + 15sqrt(5) = 17sqrt(5)
Therefore, the simplified expression is 17sqrt(5).
So, the correct answer is D. 17sqrt(5).
sqrt(125) = sqrt(25 * 5) = sqrt(5) * 5 = 5sqrt(5)
Now, the expression becomes:
2sqrt(5) + 3sqrt(125) = 2sqrt(5) + 3(5sqrt(5))
Now multiply 3 by 5sqrt(5):
2sqrt(5) + 15sqrt(5)
Now combine like terms:
2sqrt(5) + 15sqrt(5) = 17sqrt(5)
Therefore, the simplified expression is 17sqrt(5).
So, the correct answer is D. 17sqrt(5).
you just said B a second ago
GPT 3.5
I apologize for the mistake. The correct simplified expression is:
2sqrt(5) + 3sqrt(125) = 2sqrt(5) + 3 * 5sqrt(5) = 2sqrt(5) + 15sqrt(5) = 17sqrt(5)
Therefore, the correct answer is D. 17sqrt(5).
2sqrt(5) + 3sqrt(125) = 2sqrt(5) + 3 * 5sqrt(5) = 2sqrt(5) + 15sqrt(5) = 17sqrt(5)
Therefore, the correct answer is D. 17sqrt(5).