Math Problem Statement

4 akar 5 + 5 akar 4

Solution

The expression you provided is:

45+544\sqrt{5} + 5\sqrt{4}

Let's simplify step by step:

  1. 5\sqrt{5} remains as is since it's an irrational number.
  2. 4=2\sqrt{4} = 2 since the square root of 4 is 2.

Now, substitute that back into the expression:

45+5×2=45+104\sqrt{5} + 5 \times 2 = 4\sqrt{5} + 10

Thus, the simplified form of the expression is:

45+104\sqrt{5} + 10

Would you like more details on any of the steps?

Related Questions:

  1. How do you simplify other square root expressions?
  2. What are irrational numbers, and why is 5\sqrt{5} one of them?
  3. How do you add or subtract terms involving square roots?
  4. Can square roots of non-perfect squares be simplified further?
  5. What is the difference between rational and irrational numbers?

Tip: When simplifying square root expressions, always look for perfect square factors to simplify them further.

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Math Problem Analysis

Mathematical Concepts

Algebra
Radical Expressions
Square Roots

Formulas

Simplifying square roots: √n
Basic operations with radicals: a√b + c√d

Theorems

Square Root Theorem
Addition of Radical Expressions

Suitable Grade Level

Grades 8-10