Answer:
[tex]2\sqrt{5}[/tex]
C is the correct option.
Step-by-step explanation:
The given expression is [tex]\sqrt{180}-\sqrt{125}+\sqrt{5}[/tex]
In order to simplify the expression, we find the factors.
180 =6 ×6×5
125 = 5 ×5×5
Hence, we can rewrite the expression as
[tex]\sqrt{6\times6\times5}-\sqrt{5\times5\times5}+\sqrt{5}[/tex]
We can further write this expression as
[tex]\sqrt{6^2\times5}-\sqrt{5^2\times5}+\sqrt{5}[/tex]
Now, we can use the rule [tex]\sqrt{x^2}=x[/tex]
[tex]6\sqrt{5}-5\sqrt{5}+\sqrt{5}[/tex]
Finally, we can combine these like terms
[tex]2\sqrt{5}[/tex]
Hence, C is the correct option.
