Math Problem Statement

simplest form of 2√2 + 5√2 + 6√2?

Solution

The expression you provided is:

22+52+622\sqrt{2} + 5\sqrt{2} + 6\sqrt{2}

To simplify this, notice that all terms involve 2\sqrt{2}, so we can factor out 2\sqrt{2} and add the coefficients:

(2+5+6)2=132(2 + 5 + 6)\sqrt{2} = 13\sqrt{2}

Thus, the simplest form of the expression is:

13213\sqrt{2}

Would you like further explanation on any steps?

Here are 5 related questions:

  1. How do you simplify expressions with square roots?
  2. What are the rules for factoring square roots from terms?
  3. Can square roots with different radicands be combined?
  4. How do you simplify more complex expressions involving multiple radicals?
  5. How do you handle square roots in algebraic equations?

Tip: When simplifying expressions with radicals, always check if you can factor out common square roots to make the calculation easier!

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Math Problem Analysis

Mathematical Concepts

Simplification
Radicals
Algebra

Formulas

a√n + b√n = (a + b)√n

Theorems

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Suitable Grade Level

Grades 7-9