Questions: Simplify. √(50 y^10) Assume that the variable y represents a positive real n

Transcript text: Simplify. \[ \sqrt{50 y^{10}} \] Assume that the variable $y$ represents a positive real $n$

Solution

Step 1: Simplifying the Expression

We start with the expression $\sqrt{50 y^{10}}$. This can be rewritten as $\sqrt{50} \cdot \sqrt{y^{10}}$.

Step 2: Breaking Down the Square Roots

Next, we simplify each part:

For $\sqrt{50}$, we can factor it as $\sqrt{25 \cdot 2} = \sqrt{25} \cdot \sqrt{2} = 5\sqrt{2}$.
For $\sqrt{y^{10}}$, we use the property of exponents: $\sqrt{y^{10}} = y^{10/2} = y^5$.

Step 3: Combining the Results

Combining these results, we have: \[ \sqrt{50 y^{10}} = 5\sqrt{2} \cdot y^5 \]

Thus, the simplified form of the expression is: \[ \boxed{5y^5\sqrt{2}} \]

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