The value of `(sqrt63 xx sqrt7)/(root3(27))` is

Options

A. 7
B. 9
C. 21
D. 18

Answer

To solve the expression \((\sqrt{63} \times \sqrt{7}) / \sqrt[3]{27}\), we can follow these steps:

### Step 1: Simplify \(\sqrt{63}\)
We start by breaking down \(\sqrt{63}\):
\[ \sqrt{63} = \sqrt{9 \times 7} = \sqrt{9} \times \sqrt{7} = 3\sqrt{7} \]

### Step 2: Simplify \(\sqrt[3]{27}\)
Next, we simplify \(\sqrt[3]{27}\):
\[ \sqrt[3]{27} = \sqrt[3]{3^3} = 3 \]

### Step 3: Substitute back into the expression
Now we substitute our simplified values back into the original expression:
\[ \frac{\sqrt{63} \times \sqrt{7}}{\sqrt[3]{27}} = \frac{3\sqrt{7} \times \sqrt{7}}{3} \]

### Step 4: Simplify the expression
We can simplify this further:
\[ = \frac{3 \times \sqrt{7} \times \sqrt{7}}{3} = \frac{3 \times 7}{3} = 7 \]

### Final Answer
Thus, the value of \((\sqrt{63} \times \sqrt{7}) / \sqrt[3]{27}\) is \(7\).

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