Question

select the correct answer.
what is this expression in simplified form?
$2\sqrt{2} \cdot 7\sqrt{18}$
a. 84
b. $84\sqrt{2}$
c. $14\sqrt{6}$
d. $18\sqrt{5}$

Explanation:

Step1: Multiply coefficients and radicals separately

First, multiply the coefficients (the numbers outside the square roots) and the radicals (the square root parts) separately. The coefficients are 2 and 7, and the radicals are $\sqrt{2}$ and $\sqrt{18}$. So we have:
$(2\times7)\times(\sqrt{2}\times\sqrt{18})$
Calculating the product of the coefficients: $2\times7 = 14$
For the radicals, we use the property $\sqrt{a}\times\sqrt{b}=\sqrt{ab}$, so $\sqrt{2}\times\sqrt{18}=\sqrt{2\times18}$

Step2: Simplify the radical

Simplify $\sqrt{2\times18}$. First, calculate $2\times18 = 36$. Then $\sqrt{36}=6$ (since $6\times6 = 36$)
Now we have $14\times6$ (because we had 14 from the coefficients and 6 from the simplified radical)

Step3: Calculate the final product

Calculate $14\times6 = 84$

Answer:

A. 84