Question

algebra i-23511200310d101
5-2: mathxl for school: additional practice
write the product in its simplest form.
\\(\sqrt{80} \cdot \sqrt{176}\\)
\\(\sqrt{80} \cdot \sqrt{176} = \square\\)
(type an exact answer, using radicals as needed.)

Explanation:

Step1: Use the property $\sqrt{a}\cdot\sqrt{b}=\sqrt{ab}$

$\sqrt{80}\cdot\sqrt{176}=\sqrt{80\times176}$

Step2: Calculate the product inside the square root

$80\times176 = 14080$

Step3: Factor 14080 into perfect squares and other factors

First, factor 14080: $14080 = 64\times220$ (since $64\times220 = 14080$)
Then, $220 = 4\times55$ (since $4\times55 = 220$)
So, $14080 = 64\times4\times55$

Step4: Simplify the square root

$\sqrt{64\times4\times55}=\sqrt{64}\times\sqrt{4}\times\sqrt{55}$
We know that $\sqrt{64} = 8$ and $\sqrt{4} = 2$
So, $8\times2\times\sqrt{55}=16\sqrt{55}$

Answer:

$16\sqrt{55}$