Question

X Which two choices are equivalent to this expression?

2√75 +3√50
x
x
A
25√6
B 10√3+15/2
C 25√3+25√2
D 2√25-3+3√25-2
E
3√25+2√25

Answer 1

B. 10√3 + 15√2.


2√75 + 3√50; both 75 and 50 have a common factor of 25, and the square root of 25 = 5.
So we can take out √25 from both terms:
2√(25*3) + 3√(25*2)
This reduces to (2*5)√3 + (3*5)√2
And simplifies to: 10√3 + 15√2.
Option B is correct.

I don’t think I see any other options that work?
2√75 = √300 since 2=√4 and √(4*75=300).
3√50 = √450 since 3=√9 and √(9*50=450).
300 and 450 have a common factor of 25, also with a sqrt of 5.
450/25 = 18 and 300/25 = 12.
The most these simplify to is:
5√18 + 5√12.

Option B is one of the correct choices.