What is 20m−−−−√⋅5n−−√

Question

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Enter the missing values in the solution. Enter variables alphabetically.

(1 point)

Answer 1

To simplify the expression $\sqrt{20m}\cdot \sqrt{5n}$, we can apply the property of square roots which states that $\sqrt{a}\cdot \sqrt{b}=\sqrt{a\cdot b}$.

Let's simplify the expression step by step:

1. Combine the square roots: $$\sqrt{20m}\cdot \sqrt{5n}=\sqrt{20m\cdot 5n}$$

2. Calculate the product inside the square root: $$20m\cdot 5n=(20\cdot 5)(m\cdot n)=100mn$$

3. Now, we have: $$\sqrt{20m}\cdot \sqrt{5n}=\sqrt{100mn}$$

4. Simplify the square root: $$\sqrt{100mn}=\sqrt{100}\cdot \sqrt{mn}=10\sqrt{mn}$$

Thus, the simplified form of the expression is: $$10\sqrt{mn}$$

So, the missing values in the solution are:

• The coefficient is 10.
• The variables are $m$ and $n$.

In alphabetical order, you would write:

• The final answer is $10\sqrt{mn}$.