Question

Which choices are equivalent to the expression below? Check all that apply.
5 square root 3

Answer 1

Answer: √75, √25 • √3, √15 • √5

Explanation:

Answer 2

Option A:
`√(75)`

Option C:
`√(15) \cdot √(5)`

Option F:
`√(25) \cdot √(3)`

Solution:

Given expression is
`5 √(3)`.

Option A:
`√(75)`

`√(75)=√(25*3)`

`=√(5^2*3)`

`=5√(3)`

Hence
`√(75)` is equivalent expression of
`5 √(3)`.

Option B:
`√(45)`

`√(45)=√(9*5)`

`=√(3^2*5)`

`=3√(5)`

Hence
`√(45)` is not equivalent expression of
`5 √(3)`.

Option C:
`√(15) \cdot √(5)`

`√(15) \cdot √(5)=√(15*5)`

`=√(75)`

`=5√(3)` (proved in option A)

Hence
`√(15) \cdot √(5)` is equivalent expression of
`5 √(3)`.

Option D:
`√(3) \cdot √(5)`

`√(3) \cdot √(5)=√(3*5)`

`=√(15)`

Hence
`√(3) \cdot √(5)` is not equivalent expression of
`5 √(3)`.

Option E: 75

75 is a whole number.

Hence 75 is not equivalent expression of
`5 √(3)`.

Option F:
`√(25) \cdot √(3)`

`√(25) \cdot √(3)=√(25*3)`

`=√(75)`

`=5√(3)` (proved in option A)

Hence
`√(25) \cdot √(3)` is equivalent expression of
`5 √(3)`.

Therefore,
`√(75),\ \ √(15) \cdot √(5), \ \ √(25) \cdot √(3)` are all equivalent expressions of
`5 √(3)`.