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Multiply and simplify \( \sqrt{10}(\sqrt{10}-\sqrt{5}) \) 10 \( 10-5 \sqrt{2} \) \( 5 \sqrt{2} \) \( \sqrt{100}-\sqrt{50} \) \( > \) Next Question

Ask by Craig Howell. in the United States
Feb 27,2025

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Answer

The simplified form is \( 10 - 5\sqrt{2} \).

Solution

We start by distributing √10 over the expression in parentheses:   √10 · √10 = √(10×10) = √100 = 10   √10 · (–√5) = –√(10×5) = –√50 Thus, the expression becomes:   10 – √50 Notice that √50 can be simplified:   √50 = √(25×2) = 5√2 So the entire expression simplifies to:   10 – 5√2 Therefore, the simplified form is 10 – 5√2.

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Bonus Knowledge

Let's take a trip back in time! The square root symbol, introduced by the mathematician Christophorus Clavius in the late 16th century, revolutionized the way we engage with numbers, especially in simplifying expressions like yours. It laid the groundwork for modern algebra, allowing for complex calculations to be simplified into beautiful, neat forms! Now, for real-world applications, understanding how to manipulate square roots can be incredibly handy! Whether you're designing a garden and need to calculate area or working on a physics problem that involves distance calculations, being able to simplify expressions swiftly can save you time and effort. It's like having a secret weapon in your mathematical toolkit!

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