The value of `3sqrt(-91125) - 3sqrt(512)` is

Options

A. `-53`
B. 42
C. 73
D. `-37`

Answer

To solve the expression \(3\sqrt[3]{-91125} - 3\sqrt[3]{512}\), we will follow these steps:

### Step 1: Find the cube root of \(-91125\)
To find \(\sqrt[3]{-91125}\), we first express \(-91125\) as a product of cubes.

Notice that:
\[ 91125 = 45^3 \]
Thus,
\[ \sqrt[3]{-91125} = \sqrt[3]{-1 \times 45^3} = \sqrt[3]{-1} \times \sqrt[3]{45^3} = -1 \times 45 = -45 \]

### Step 2: Find the cube root of \(512\)
Next, we find \(\sqrt[3]{512}\).

We know that:
\[ 512 = 8^3 \]
Thus,
\[ \sqrt[3]{512} = \sqrt[3]{8^3} = 8 \]

### Step 3: Substitute the values back into the expression
Now we can substitute the values we found back into the original expression:
\[ 3\sqrt[3]{-91125} - 3\sqrt[3]{512} = 3(-45) - 3(8) \]

### Step 4: Simplify the expression
Now we simplify:
\[ = -135 - 24 \]
\[ = -159 \]

### Final Answer
Thus, the value of \(3\sqrt[3]{-91125} - 3\sqrt[3]{512}\) is \(-159\).

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