Math Problem Statement

9√3 + 2√3. Add. Write your answer in simplest form.

Solution

The given expression is 93+239\sqrt{3} + 2\sqrt{3}.

Since both terms involve 3\sqrt{3}, you can combine them by adding the coefficients of 3\sqrt{3}. The operation is similar to adding like terms in algebra:

93+23=(9+2)3=1139\sqrt{3} + 2\sqrt{3} = (9 + 2)\sqrt{3} = 11\sqrt{3}

So, the answer in simplest form is:

113\boxed{11\sqrt{3}}

Would you like a further breakdown or have any additional questions?

Here are some related questions to consider:

  1. How do you simplify expressions involving square roots?
  2. What happens if the square roots are different, like 2\sqrt{2} and 3\sqrt{3}?
  3. How can you rationalize a denominator if it involves a square root?
  4. How would you handle subtraction with square roots like 93239\sqrt{3} - 2\sqrt{3}?
  5. Can you simplify an expression like 512+335\sqrt{12} + 3\sqrt{3}?

Tip: When adding or subtracting square roots, make sure they are the same radical (like 3\sqrt{3}) before combining.

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Math Problem Analysis

Mathematical Concepts

Algebra
Radicals
Simplifying Expressions

Formulas

a√b + c√b = (a + c)√b

Theorems

Properties of Square Roots
Like Terms in Radical Expressions

Suitable Grade Level

Grades 7-9