If `xy = 2, xz = 8 and yz = 5`, then the value of xyz is closest to:

Options

A. 5
B. 9
C. 15
D. 25

Answer

To solve the problem, we are given three equations:

1. \( xy = 2 \) (Equation 1)
2. \( xz = 8 \) (Equation 2)
3. \( yz = 5 \) (Equation 3)

We want to find the value of \( xyz \).

### Step-by-Step Solution:

**Step 1: Multiply all three equations together.**

We multiply the left-hand sides and the right-hand sides of the equations:

\[ (xy)(xz)(yz) = (2)(8)(5) \]

This simplifies to:

\[ x^2y^2z^2 = 80 \]

**Step 2: Take the square root of both sides.**

To find \( xyz \), we take the square root of both sides:

\[ xyz = \sqrt{80} \]

**Step 3: Simplify \( \sqrt{80} \).**

We can simplify \( \sqrt{80} \):

\[ \sqrt{80} = \sqrt{16 \times 5} = \sqrt{16} \times \sqrt{5} = 4\sqrt{5} \]

**Step 4: Estimate \( \sqrt{5} \).**

We know that \( \sqrt{5} \) is approximately \( 2.236 \). Therefore:

\[ xyz \approx 4 \times 2.236 = 8.944 \]

**Step 5: Round to the nearest whole number.**

The value \( 8.944 \) is closest to \( 9 \).

### Final Answer:

Thus, the value of \( xyz \) is closest to \( 9 \).

---