Math Problem Statement

(3+√3)(2-√2)

Solution

To simplify the expression (3+3)(22)(3 + \sqrt{3})(2 - \sqrt{2}), use the distributive property (FOIL method):

(3+3)(22)=(32)+(32)+(32)+(32)(3 + \sqrt{3})(2 - \sqrt{2}) = (3 \cdot 2) + (3 \cdot -\sqrt{2}) + (\sqrt{3} \cdot 2) + (\sqrt{3} \cdot -\sqrt{2})

Simplify each term:

  1. 32=63 \cdot 2 = 6
  2. 32=323 \cdot -\sqrt{2} = -3\sqrt{2}
  3. 32=23\sqrt{3} \cdot 2 = 2\sqrt{3}
  4. 32=6\sqrt{3} \cdot -\sqrt{2} = -\sqrt{6} (since ab=ab\sqrt{a} \cdot \sqrt{b} = \sqrt{ab})

Now, combine the terms:

632+2366 - 3\sqrt{2} + 2\sqrt{3} - \sqrt{6}

This is the simplified form:

632+236\boxed{6 - 3\sqrt{2} + 2\sqrt{3} - \sqrt{6}}

Would you like me to break down any part of this further or show additional details? 😊


Related Questions:

  1. How do you simplify expressions involving surds like a\sqrt{a}?
  2. What is the distributive property, and how is it applied in algebra?
  3. How do you combine terms with different roots or surds?
  4. How can this be expressed as an approximate decimal value?
  5. How can this process be visualized geometrically?

Tip:

When simplifying expressions with square roots, always look for opportunities to combine like terms or rationalize denominators where possible!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Radicals
Distributive Property

Formulas

Distributive Property: (a + b)(c + d) = ac + ad + bc + bd
Multiplication of Square Roots: √a * √b = √(a*b)

Theorems

Distributive Property

Suitable Grade Level

Grades 8-10