Problem 110
Question
Explain how to simplify \(\sqrt{10} \cdot \sqrt{5}\)
Step-by-Step Solution
Verified Answer
The simplified form of \( \sqrt{10} \cdot \sqrt{5}\) is \(5 \sqrt{2}\).
1Step 1: Apply the multiplication property of radicals
Write \(\sqrt{10} \cdot \sqrt{5}\) as the square root of their product, \( \sqrt{10 \cdot 5}\).
2Step 2: Calculate the product
Calculate \( 10 \cdot 5 \) which equals 50. So now we have \( \sqrt{50}\).
3Step 3: Simplify the square root
The number 50 can be factored into 25 and 2, where 25 is a perfect square, so \( \sqrt{50} \) becomes \( \sqrt{25 \cdot 2} \).
4Step 4: Further simplify the square root
Since the square root of 25 is 5, \( \sqrt{25 \cdot 2}\) simplifies to \( 5 \sqrt{2} \).
Other exercises in this chapter
Problem 109
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