$$ 5 \sqrt{6 x} $$ and $$ -6 \sqrt{24 x} $$

Question

UpStudy AI · Accepted Answer

It looks like you have two radical expressions:

1. $$ 5 \sqrt{6x} $$
2. $$ -6 \sqrt{24x} $$

Let's simplify and combine them.

### Step 1: Simplify Each Radical

First, simplify $$ \sqrt{24x} $$:

$$
\sqrt{24x} = \sqrt{4 \times 6x} = \sqrt{4} \times \sqrt{6x} = 2 \sqrt{6x}
$$

### Step 2: Substitute Back into the Expression

Now, substitute the simplified form back into the original expression:

$$
5 \sqrt{6x} - 6 \sqrt{24x} = 5 \sqrt{6x} - 6 \times 2 \sqrt{6x}
$$

$$
= 5 \sqrt{6x} - 12 \sqrt{6x}
$$

### Step 3: Combine Like Terms

Combine the terms by factoring out $$ \sqrt{6x} $$:

$$
5 \sqrt{6x} - 12 \sqrt{6x} = (5 - 12) \sqrt{6x} = -7 \sqrt{6x}
$$

### Final Simplified Expression

$$
-7 \sqrt{6x}
$$

**Therefore, the simplified form of the given expressions is:**

$$
-7 \sqrt{6x}
$$
The simplified form is $$ -7 \sqrt{6x} $$.

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