Math Problem Statement

Latihan Soal: Selesaikanlah! 1. 2√3 + √3 2. √8 + √2 3. √32 - √8 4. ³√8 5. ³√64

Solution

Let's solve each of the problems in the image one by one.

  1. 23+32\sqrt{3} + \sqrt{3}

    • Combine like terms: 23+3=332\sqrt{3} + \sqrt{3} = 3\sqrt{3}.

    Answer: 333\sqrt{3}

  2. 8+2\sqrt{8} + \sqrt{2}

    • Simplify 8=4×2=22\sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2}.
    • Now add the terms: 22+2=322\sqrt{2} + \sqrt{2} = 3\sqrt{2}.

    Answer: 323\sqrt{2}

  3. 328\sqrt{32} - \sqrt{8}

    • Simplify 32=16×2=42\sqrt{32} = \sqrt{16 \times 2} = 4\sqrt{2}.
    • Simplify 8=22\sqrt{8} = 2\sqrt{2}.
    • Now subtract: 4222=224\sqrt{2} - 2\sqrt{2} = 2\sqrt{2}.

    Answer: 222\sqrt{2}

  4. 83\sqrt[3]{8}

    • 83=2\sqrt[3]{8} = 2, because 23=82^3 = 8.

    Answer: 22

  5. 643\sqrt[3]{64}

    • 643=4\sqrt[3]{64} = 4, because 43=644^3 = 64.

    Answer: 44

Would you like further explanations or details on any of these solutions?

Here are 5 follow-up questions you could explore:

  1. How would you simplify 53+435\sqrt{3} + 4\sqrt{3}?
  2. What is 50+2\sqrt{50} + \sqrt{2}?
  3. Can you calculate 1253\sqrt[3]{125}?
  4. How do you rationalize 13\frac{1}{\sqrt{3}}?
  5. What is 182\sqrt{18} - \sqrt{2}?

Tip: When dealing with square roots, always look for perfect square factors to simplify expressions easily.

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Math Problem Analysis

Mathematical Concepts

Simplifying square roots
Adding square roots
Cube roots
Basic algebra

Formulas

√(a * b) = √a * √b
³√x = number such that (number)^3 = x

Theorems

Properties of square roots
Properties of cube roots

Suitable Grade Level

Grades 6-8