Math Problem Statement

3(2 - 3√18)

Solution

Let's simplify the expression:

3(2318)3(2 - 3\sqrt{18})

Step 1: Simplify the square root

We know that: 18=9×2=32\sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2}

So, the expression becomes: 3(23×32)=3(292)3(2 - 3 \times 3\sqrt{2}) = 3(2 - 9\sqrt{2})

Step 2: Distribute the 3

Now, distribute the 3 across the terms inside the parentheses: 3×23×92=62723 \times 2 - 3 \times 9\sqrt{2} = 6 - 27\sqrt{2}

Thus, the simplified expression is: 62726 - 27\sqrt{2}

Let me know if you'd like more details on this process or have any further questions!

Related questions:

  1. How do you simplify square roots with large numbers?
  2. What is the process for distributing multiplication over subtraction?
  3. Can you explain how to combine like terms with square roots?
  4. How do you factor expressions that involve square roots?
  5. What is the difference between rational and irrational numbers?

Tip: When simplifying square roots, try breaking the number into prime factors to check if any can be simplified easily.

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Math Problem Analysis

Mathematical Concepts

Simplifying Expressions
Square Roots
Distributive Property

Formulas

√ab = √a × √b
Distributive Property: a(b - c) = ab - ac

Theorems

Distributive Property
Properties of Square Roots

Suitable Grade Level

Grades 8-10