Question

simplify.
\sqrt{45} \times 2\sqrt{80}

Explanation:

Step1: Simplify each square root

First, simplify $\sqrt{45}$ and $\sqrt{80}$ by factoring out perfect squares.
For $\sqrt{45}$, we have $45 = 9\times5$, so $\sqrt{45}=\sqrt{9\times5}=\sqrt{9}\times\sqrt{5}=3\sqrt{5}$.
For $\sqrt{80}$, we have $80 = 16\times5$, so $\sqrt{80}=\sqrt{16\times5}=\sqrt{16}\times\sqrt{5}=4\sqrt{5}$.

Step2: Substitute back into the original expression

The original expression is $\sqrt{45}\times2\sqrt{80}$. Substituting the simplified square roots, we get:
$(3\sqrt{5})\times2\times(4\sqrt{5})$

Step3: Multiply the coefficients and the square roots separately

First, multiply the coefficients: $3\times2\times4 = 24$.
Then, multiply the square roots: $\sqrt{5}\times\sqrt{5}=\sqrt{5\times5}=\sqrt{25}=5$.

Step4: Multiply the results from Step3

Now, multiply the coefficient result and the square root result: $24\times5 = 120$.

Answer:

120