If `sqrt6 xx sqrt15 = x sqrt10` , then the value of x is

Options

A. 3
B. ` pm 3`
C. `sqrt3`
D. `sqrt6`

Answer

To solve the equation \( \sqrt{6} \times \sqrt{15} = x \sqrt{10} \), we will follow these steps:

### Step 1: Simplify the left side of the equation
We can use the property of square roots that states \( \sqrt{a} \times \sqrt{b} = \sqrt{a \times b} \).

\[ \sqrt{6} \times \sqrt{15} = \sqrt{6 \times 15} \]

### Step 2: Calculate \( 6 \times 15 \)
Now we calculate \( 6 \times 15 \):

\[ 6 \times 15 = 90 \]

### Step 3: Write the left side in terms of square roots
Now we can rewrite the left side:

\[ \sqrt{90} = x \sqrt{10} \]

### Step 4: Simplify \( \sqrt{90} \)
Next, we simplify \( \sqrt{90} \). We can factor \( 90 \) into its prime factors:

\[ 90 = 9 \times 10 = 3^2 \times 10 \]

Thus, we have:

\[ \sqrt{90} = \sqrt{9 \times 10} = \sqrt{9} \times \sqrt{10} = 3 \sqrt{10} \]

### Step 5: Set the equation
Now we can set the equation:

\[ 3 \sqrt{10} = x \sqrt{10} \]

### Step 6: Divide both sides by \( \sqrt{10} \)
To isolate \( x \), we divide both sides by \( \sqrt{10} \):

\[ \frac{3 \sqrt{10}}{\sqrt{10}} = x \]

This simplifies to:

\[ x = 3 \]

### Final Answer
Thus, the value of \( x \) is \( 3 \).

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