Let's go through the process of expanding and simplifying -√2 (√2 + √3) step by step.
Step 1: Understand the expression
The expression is -√2 multiplied by the quantity (√2 + √3). This means we need to use the distributive property: multiply -√2 by each term inside the bracket.
Step 2: Apply the distributive property
Multiply -√2 by √2 and then by √3:
- -√2 × √2 = - (√2 × √2)
- -√2 × √3 = - (√2 × √3)
Step 3: Simplify each multiplication
Recall that √a × √a = a. So, simplify each part:
- √2 × √2 = 2, so -√2 × √2 = -2
- √2 × √3 = √6 (since you multiply inside the root: √(2×3) = √6), so -√2 × √3 = -√6
Step 4: Write the simplified expression
After simplifying, the expression becomes:
-2 - √6
Final answer:
-√2 (√2 + √3) = -2 - √6
This is the expression expanded and simplified in surd form.