Question

What is the exact value of the expressions the square root of 180. − the square root 125. + the square root of 5.? Simplify if possible.
A) 2the square root of 2.
B) 12the square root of 2.
C) 2the square root of 5.
D) 12the square root of 5.

Answer 1

Answer:

$2\sqrt{5}$

C is the correct option.

Step-by-step explanation:

The given expression is $\sqrt{180}-\sqrt{125}+\sqrt{5}$

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

$\sqrt{6\times6\times5}-\sqrt{5\times5\times5}+\sqrt{5}$

We can further write this expression as

$\sqrt{6^2\times5}-\sqrt{5^2\times5}+\sqrt{5}$

Now, we can use the rule $\sqrt{x^2}=x$

$6\sqrt{5}-5\sqrt{5}+\sqrt{5}$

Finally, we can combine these like terms

$2\sqrt{5}$

Hence, C is the correct option.

Answer 2

I hope this helps you