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Chapter 8: Problem 126

Explain how to simplify \(\sqrt{10} \cdot \sqrt{5}\)

Short Answer

Expert verified
So, \(\sqrt{10} \cdot \sqrt{5}\) simplifies to \(5\sqrt{2}\)

Step by step solution

01

Identify the expression

The given expression is \(\sqrt{10} \cdot \sqrt{5}\)
02

Apply the property of square roots

We know that \(\sqrt{a} \cdot \sqrt{b}\) equals \(\sqrt{a \cdot b}\). So, we will simplify \(\sqrt{10} \cdot \sqrt{5}\) as \(\sqrt{10 \cdot 5}\)
03

Compute the multiplication

Now, we calculate the multiplication in the square root. So, it becomes \(\sqrt{50}\)
04

Simplify the square root

Last, simplify \(\sqrt{50}\) by breaking down 50 into its prime factors. 50 can be written as 5*2*5, so \(\sqrt{50}\) simplifies to \(5 \cdot \sqrt{2}\)

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