Math Problem Statement

Hasil dari \( \frac{8 \sqrt{72}}{2 \sqrt{18}} \) adalah ...

Solution

The text from the image reads:

"27. Hasil dari 872218\frac{8 \sqrt{72}}{2 \sqrt{18}} adalah ..."

This is a mathematical expression asking for the result of the fraction 872218\frac{8 \sqrt{72}}{2 \sqrt{18}}.

Let's solve this step by step:

  1. Simplify the square roots:

    • 72=36×2=62\sqrt{72} = \sqrt{36 \times 2} = 6\sqrt{2}
    • 18=9×2=32\sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2}
  2. Substitute the simplified square roots into the expression: 8×622×32=48262\frac{8 \times 6\sqrt{2}}{2 \times 3\sqrt{2}} = \frac{48\sqrt{2}}{6\sqrt{2}}

  3. Cancel out the common terms (the 2\sqrt{2} cancels out): 486=8\frac{48}{6} = 8

Thus, the result of 872218\frac{8 \sqrt{72}}{2 \sqrt{18}} is 8.

Would you like further explanation on any steps?

Here are five related questions to practice:

  1. Simplify 105052\frac{10 \sqrt{50}}{5 \sqrt{2}}.
  2. What is 72×18\sqrt{72} \times \sqrt{18}?
  3. Simplify 122446\frac{12 \sqrt{24}}{4 \sqrt{6}}.
  4. Solve 5982\frac{5 \sqrt{98}}{\sqrt{2}}.
  5. How do you simplify 32\sqrt{32}?

Tip: When simplifying square roots, always look for perfect square factors (like 4, 9, 16, etc.).

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Math Problem Analysis

Mathematical Concepts

Simplification of Radicals
Algebra
Fraction Simplification

Formulas

Simplifying square roots: \( \sqrt{ab} = \sqrt{a} \times \sqrt{b} \)
Basic fraction: \( \frac{a}{b} \)

Theorems

Radical Simplification

Suitable Grade Level

Grades 7-10