Question

find the area of the following rectangle. give your answer in simplest form. hint: to add the square root symbol (√), type
oot\

Explanation:

Step1: Recall area formula

The area formula for a rectangle is $A = l\times w$, where $l$ is the length and $w$ is the width. Here, $l = 4\sqrt{30}$ and $w=2\sqrt{66}$.

Step2: Multiply the length and width

$A=(4\sqrt{30})\times(2\sqrt{66})$. Using the property $\sqrt{a}\times\sqrt{b}=\sqrt{ab}$ and $(a\sqrt{m})\times(b\sqrt{n})=(a\times b)\sqrt{m\times n}$, we have $A=(4\times2)\sqrt{30\times66}$.

Step3: Simplify the product inside the square - root

First, calculate $30\times66 = 1980$. Then, factorize $1980$: $1980=2\times2\times3\times3\times5\times11$. So, $\sqrt{1980}=\sqrt{2^{2}\times3^{2}\times5\times11}=2\times3\sqrt{55}=6\sqrt{55}$.

Step4: Calculate the final area

$A = 8\times6\sqrt{55}=48\sqrt{55}$.

Answer:

$48\sqrt{55}$