Math Problem Statement

2 root 2 + 5 root 9

Solution

To solve the expression 22+592\sqrt{2} + 5\sqrt{9}:

  1. Simplify the square roots:

    • 2\sqrt{2} remains 2\sqrt{2} because it's already in its simplest form.
    • 9=3\sqrt{9} = 3 because 9=329 = 3^2.
  2. Substitute the simplified values back into the expression: 22+59=22+5×32\sqrt{2} + 5\sqrt{9} = 2\sqrt{2} + 5 \times 3

  3. Multiply 55 by 33: 5×3=155 \times 3 = 15

  4. Combine the terms: 22+152\sqrt{2} + 15

So, the simplified expression is 22+152\sqrt{2} + 15.

Would you like more details or have any questions?

Here are some related questions to expand on this concept:

  1. What is 32+493\sqrt{2} + 4\sqrt{9}?
  2. How do you simplify 18+28\sqrt{18} + 2\sqrt{8}?
  3. What is 22+342\sqrt{2} + 3\sqrt{4}?
  4. If you have 75+2257\sqrt{5} + 2\sqrt{25}, what is the result?
  5. How do you add 22+582\sqrt{2} + 5\sqrt{8}?
  6. What is 43+2274\sqrt{3} + 2\sqrt{27}?
  7. How do you simplify 50+52\sqrt{50} + 5\sqrt{2}?
  8. What is 311+2993\sqrt{11} + 2\sqrt{99}?

Tip: When simplifying expressions with square roots, always simplify the square roots first before performing any other operations.

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Math Problem Analysis

Mathematical Concepts

Square Roots

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9