Math Problem Statement

Manakah pasangan bentuk akar irasional dan akar rasional secara berurutan dari pasangan berikut?

Solution

The problem presented asks for the identification of pairs of irrational and rational square roots, in order, from the given expressions. Let's evaluate each pair:

  1. 11\sqrt{11} and 49\sqrt{49}

    • 11\sqrt{11} is irrational.
    • 49=7\sqrt{49} = 7, which is rational.

    This pair matches the condition: irrational followed by rational.

  2. 2\sqrt{2} and 24\sqrt{24}

    • 2\sqrt{2} is irrational.
    • 24\sqrt{24} simplifies to 262\sqrt{6}, which is still irrational.

    This pair does not match the condition.

  3. 64\sqrt{64} and 36\sqrt{36}

    • 64=8\sqrt{64} = 8, which is rational.
    • 36=6\sqrt{36} = 6, which is also rational.

    This pair does not match the condition (both are rational).

  4. 7\sqrt{7} and 64\sqrt{64}

    • 7\sqrt{7} is irrational.
    • 64=8\sqrt{64} = 8, which is rational.

    This pair matches the condition: irrational followed by rational.

  5. 3\sqrt{3} and 5\sqrt{5}

    • Both 3\sqrt{3} and 5\sqrt{5} are irrational.

    This pair does not match the condition.

Conclusion:

The pairs that match the condition of irrational and rational square roots in sequence are:

  • 11\sqrt{11} and 49\sqrt{49}
  • 7\sqrt{7} and 64\sqrt{64}

Would you like more details or further clarifications?

Related Questions:

  1. What defines an irrational number?
  2. How can we simplify square roots of non-perfect squares?
  3. Why are some square roots irrational while others are rational?
  4. What other methods exist for identifying rational and irrational numbers?
  5. How does the property of square roots relate to exponents?

Tip: To determine if a square root is rational, check if the number is a perfect square (like 49 or 64). Non-perfect squares lead to irrational results.

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Math Problem Analysis

Mathematical Concepts

Irrational Numbers
Rational Numbers
Square Roots

Formulas

√n (square root of n)

Theorems

Definition of Rational and Irrational Numbers

Suitable Grade Level

Grades 7-9