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Multiplying and Dividing Square Roots

Learn how to multiply and divide square roots, like 4.8×10\sqrt{4.8} \times \sqrt{10} and 36÷25\sqrt{36} \div \sqrt{25}, and simplify the result using rules. Let’s get started! 🚀

Multiplying and Dividing Square Roots - introduction visual

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Multiplying and Dividing Square Roots poster

Flashcards

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Square root rules for multiplication and division showing √a × √b = √(ab) and √a ÷ √b = √(a/b)Multiplying square roots step by step: √18 simplified to 3√2 and √4.8 × √10 simplified to 4√3Dividing square roots examples: √(36/25) = 6/5 = 1.2 and √50 ÷ √2 = √25 = 5

🛎️ Square Root Rules: Multiply and Divide

  • To multiply square roots, a×b=ab\sqrt{a}\times\sqrt{b}=\sqrt{ab}.
  • To divide square roots, ab=ab\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b}}.

🛎️ Multiplying Square Roots

  • Example 1: 18=9⋅2=32\sqrt{18}=\sqrt{9\cdot2}=3\sqrt{2}.
  • Example 2: 4.8×10=48=43\sqrt{4.8}\times\sqrt{10}=\sqrt{48}=4\sqrt{3}.

🛎️ Dividing Square Roots

  • Example 1: 3625=3625=65=1.2\sqrt{\frac{36}{25}}=\frac{\sqrt{36}}{\sqrt{25}}=\frac{6}{5}=1.2.
  • Example 2: 502=502=25=5\frac{\sqrt{50}}{\sqrt{2}}=\sqrt{\frac{50}{2}}=\sqrt{25}=5.

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