xpress in simplest radical form. $$ -10 \sqrt{45}+5 \sqrt{20} $$

Question

UpStudy AI · Accepted Answer

We start with the expression:

$$
-10 \sqrt{45} + 5 \sqrt{20}
$$

**Step 1.** Simplify $$\sqrt{45}$$:  
Since $$45 = 9 \times 5$$ and $$9$$ is a perfect square, we have:

$$
\sqrt{45} = \sqrt{9 \times 5} = \sqrt{9} \sqrt{5} = 3\sqrt{5}
$$

Thus,

$$
-10\sqrt{45} = -10 \times 3\sqrt{5} = -30\sqrt{5}
$$

**Step 2.** Simplify $$\sqrt{20}$$:  
Since $$20 = 4 \times 5$$ and $$4$$ is a perfect square, we have:

$$
\sqrt{20} = \sqrt{4 \times 5} = \sqrt{4} \sqrt{5} = 2\sqrt{5}
$$

Thus,

$$
5\sqrt{20} = 5 \times 2\sqrt{5} = 10\sqrt{5}
$$

**Step 3.** Combine like terms:  
Now, substitute the simplified terms back:

$$
-30\sqrt{5} + 10\sqrt{5}
$$

Since both terms have $$\sqrt{5}$$, combine their coefficients:

$$
-30 + 10 = -20
$$

Thus, the expression simplifies to:

$$
-20\sqrt{5}
$$
$$-20\sqrt{5}$$

xpress in simplest radical form. \[ -10 \sqrt{45}+5 \sqrt{20} \]