Math Problem Statement

Simplify the expression 2 + √3 - 2√3 + 1.

Solution

The expression in the image is:

2+323+12 + \sqrt{3} - 2\sqrt{3} + 1

To simplify this, let's combine like terms.

  1. Combine the constants: 2+1=32 + 1 = 3

  2. Combine the terms with 3\sqrt{3}: 323=3\sqrt{3} - 2\sqrt{3} = -\sqrt{3}

So, the simplified expression is:

333 - \sqrt{3}

Would you like further details or explanations?

Here are some related questions that could extend your understanding:

  1. What if the expression included another square root term, like 2\sqrt{2}?
  2. How do we simplify expressions involving cube roots?
  3. What if there were imaginary numbers in this expression? How would we handle them?
  4. How can we rationalize a denominator with terms like 3\sqrt{3}?
  5. How does simplifying radicals help in real-life applications?

Tip: Always look for like terms, especially with radicals and constants, to make expressions simpler.

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Math Problem Analysis

Mathematical Concepts

Algebra
Radicals
Simplification of Expressions

Formulas

Combining like terms

Theorems

Properties of Radicals

Suitable Grade Level

Grades 8-10