Question

12 (a) part a: the area of rectangle 2 can be found using the expression (5√15)(4√6). which of the following is the simplest form of the expression? a 80√15 b 40√15 c 20√90 d 20√15 (b) part b: the perimeter of rectangle 1 can be found using the expression 2(√27x)+2(2√3x). which of the following is the simplest form of the expression? a 6√30x b 7√3x c 10√3x d 2√27x + 4√3x

Explanation:

Step1: Simplify the area expression in Part A

Multiply the coefficients and the square - roots separately. $(5\sqrt{10})(4\sqrt{6})=(5\times4)\times\sqrt{10\times6}=20\sqrt{60}$. Then simplify $\sqrt{60}=\sqrt{4\times15}=2\sqrt{15}$, so $20\sqrt{60}=20\times2\sqrt{15}=40\sqrt{15}$.

Step2: Simplify the perimeter expression in Part B

First, simplify $\sqrt{27z}=\sqrt{9\times3z}=3\sqrt{3z}$. Then $2(\sqrt{27z})+2(2\sqrt{3z}) = 2\times3\sqrt{3z}+4\sqrt{3z}=6\sqrt{3z}+4\sqrt{3z}=10\sqrt{3z}$.

Answer:

(A) B. $40\sqrt{15}$
(B) C. $10\sqrt{3z}$