Question

Part 1: Find the perimeter of a rectangular object which has a length of squareroot 128 feet and a width of squareroot 200 feet. (3 points)

Part 2: Explain, in complete sentences, how you arrived at the answer and give the final solution in simplified radical form. (2 points)

Part 3: What type of object in your home or school might this be? (1 point) show work

Answer 1

the perimeter of a rectangle is adding up 4 sides

2 sides of sqrt128 each, plus 2 sides of sqrt200 each

Answer 2

to simplify them, just determine their perfect square factors

Answer 3

can you teach me how to determine their perfect square factors please

Answer 4

let's take \[\sqrt{192}\]
I can write it down in this way:\[\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt3=8\sqrt3\]
I cannot do that with 3 so I leave it in that form
Can you do that with sqrt 128 and sqrt 200?

Answer 5

sqrt 128= sqrt 64*2 = 8sqrt2? is that right :(

Answer 6

yes

Answer 7

what about sqrt200 ?

Answer 8

sqrt200= sqrt100*2 = 10sqrt2? :(

Answer 9

very good :)

Answer 10

\[P=2\left( \sqrt{128} +\sqrt{200}\right)\]
\[=2\left( \sqrt{64*2}+\sqrt{100*2} \right)\]
\[=2\left( \sqrt{8^{2}*2}+\sqrt{10^{2}*2} \right)\]
\[=2\left( 8\sqrt{2}+10\sqrt{2}\right)=2*18\sqrt{2}=36\sqrt{2}\]
i think now it is clear.

Answer 11

so basically you just add the outside numbers and keep the 2 inside the radical?

Answer 12

and thats my perimeter?

Answer 13

yes

Answer 14

3 apples + 4 apples = 7 apples
so 8sqrt2 + 10sqrt2=18 sqrt2

Answer 15

you can add or subtract only if we have the same number under the radical sign.

Answer 16

wait im confused is it 18sqrt2 or 36sqrt2

Answer 17

the perimeter is 36sqrt2

Answer 18

Thank you both so much i understand now (: