https://file.aiquickdraw.com/mathbot/file/1728722765998py3opbby.jpg

The problem provided defines \( X = \sqrt{8} \), \( Y = \sqrt{12} \), and \( Z = 3\sqrt{2} \). It asks for the result of the expression \( XY + YZ - XZ \).

Let's break this down step by step.

### Step 1: Simplifying \( X \), \( Y \), and \( Z \)
- \( X = \sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2} \)
- \( Y = \sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3} \)
- \( Z = 3\sqrt{2} \)

### Step 2: Calculating \( XY \)
\[
XY = (2\sqrt{2})(2\sqrt{3}) = 4\sqrt{6}
\]

### Step 3: Calculating \( YZ \)
\[
YZ = (2\sqrt{3})(3\sqrt{2}) = 6\sqrt{6}
\]

### Step 4: Calculating \( XZ \)
\[
XZ = (2\sqrt{2})(3\sqrt{2}) = 6\sqrt{4} = 6 \times 2 = 12
\]

### Step 5: Calculating \( XY + YZ - XZ \)
Now, substitute the values:
\[
XY + YZ - XZ = 4\sqrt{6} + 6\sqrt{6} - 12
\]
\[
= (4 + 6)\sqrt{6} - 12
\]
\[
= 10\sqrt{6} - 12
\]

### Final Answer:
The result is \( 10\sqrt{6} - 12 \), which corresponds to option **b**.

Would you like any further details or explanations?

### Related Questions:
1. What is the simplified form of \( \sqrt{18} \)?
2. How do you multiply two square roots, like \( \sqrt{a} \times \sqrt{b} \)?
3. What is the result of \( (2\sqrt{2})^2 \)?
4. How do you rationalize the denominator in an expression like \( \frac{1}{\sqrt{5}} \)?
5. How do you solve expressions involving roots and exponents?

### Tip:
When multiplying square roots, \( \sqrt{a} \times \sqrt{b} = \sqrt{a \times b} \). Always look to simplify the numbers inside the square roots first.

Given X = sqrt(8), Y = sqrt(12), Z = 3sqrt(2), find the result of XY + YZ - XZ.

Learn how to simplify an expression involving radicals: XY + YZ - XZ, where X = sqrt(8), Y = sqrt(12), and Z = 3sqrt(2). Step-by-step solution using the multiplication of square roots and properties of radicals. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation