Math Problem Statement

Simplify 10√3 + 4√2

Solution

The expression shown in the image is:

103+4210\sqrt{3} + 4\sqrt{2}

Since the terms involve different square roots, they cannot be simplified further by combining them. The final simplified form remains:

103+4210\sqrt{3} + 4\sqrt{2}

If you are looking for a numerical approximation, we can calculate:

31.732and21.414\sqrt{3} \approx 1.732 \quad \text{and} \quad \sqrt{2} \approx 1.414

Now:

10310×1.732=17.3210\sqrt{3} \approx 10 \times 1.732 = 17.32 424×1.414=5.6564\sqrt{2} \approx 4 \times 1.414 = 5.656

Thus, the approximate sum is:

17.32+5.65622.97617.32 + 5.656 \approx 22.976

Would you like more details or a specific numerical result?


Here are some related questions:

  1. How do you simplify expressions involving square roots?
  2. Can you combine terms with different square roots in any situation?
  3. How do you calculate the square root of non-perfect squares?
  4. What are some common approximations of irrational numbers like 2\sqrt{2} and 3\sqrt{3}?
  5. What are some real-world applications of simplifying square root expressions?

Tip: When working with square roots, always check if you can factor out perfect squares to further simplify the expression.

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Math Problem Analysis

Mathematical Concepts

Simplifying Square Roots
Algebra
Irrational Numbers

Formulas

√3 ≈ 1.732
√2 ≈ 1.414

Theorems

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Suitable Grade Level

Grades 8-10