Question

What is the perimeter of a computer graphic with sides measuring?
2√18, 2√32, 2√50, and 3√12 centimeters

The perimeter is _______ centimeters.

Answer 1

here we have to compute this sum:
\[\begin{gathered}
perimeter = 2\sqrt {18} + 2\sqrt {32} + 2\sqrt {50} + 3\sqrt {12} = \hfill \\
= 6\sqrt 2 + 8\sqrt 2 + 10\sqrt 2 + 6\sqrt 3 = ...? \hfill \\
\end{gathered} \]

Answer 2

okay

Answer 3

so, simplifying that expression, we get:
\[perimeter = 24\sqrt 2 + 6\sqrt 3 = ...?\]

Answer 4

ok

Answer 5

now, you have to use a calculator, in order to evaluate that numeric expression. What do you get?

Answer 6

should it be in decimal

Answer 7

yes! We have:
\[\begin{gathered}
\sqrt 2 \cong {\text{1}}{\text{,414}} \hfill \\
\sqrt 3 \cong {\text{1}}{\text{,732}} \hfill \\
\end{gathered} \]

Answer 8

okay

Answer 9

im lost doing these problems

Answer 10

so, substituting, we get:
\[perimeter = 24\sqrt 2 + 6\sqrt 3 = \left( {24 \times {\text{1}}{\text{.414}}} \right){\text{ + }}\left( {{\text{6}} \times {\text{1}}{\text{.732}}} \right) = ...?\]

Answer 11

please continue

Answer 12

okay so you want me add 24 x 1414 + 6 x 1732

Answer 13

not precisely. I meant this:
24 x 1.414 + 6 x 1.732=...?

Answer 14

there
1.414 stands for (1414/1000), and:
1.732 stands for (1732/1000)

Answer 15

ok

Answer 16

so you want me times 24 x 1.414 + 6 x 1.732

Answer 17

ok!

Answer 18

44.328

Answer 19

that's right!

Answer 20

awesome i like the way you explained this

Answer 21

thanks!

Answer 22

i will be back i got like 5 problems im stuck on but did 50 on my own and got a good grade but gotta get these last done

Answer 23

i wanted to ask you how would i make that to a radical

Answer 24

it is simple, as I wrote, before, the perimeter is:
\[perimeter = 2\sqrt {18} + 2\sqrt {32} + 2\sqrt {50} + 3\sqrt {12} \]

Answer 25

ok

Answer 26

now we can write this:
\[\begin{gathered}
2\sqrt {32} = 2\sqrt {{4^2} \times 2} = 2 \times 4\sqrt 2 = 8\sqrt 2 \hfill \\
2\sqrt {50} = 2\sqrt {{5^2} \times 2} = 2 \times 5\sqrt 2 = 10\sqrt 2 \hfill \\
3\sqrt {12} = 3\sqrt {{2^2} \times 3} = 3 \times 2\sqrt 3 = 6\sqrt 3 \hfill \\
\end{gathered} \]

Answer 27

furthermore, we have:
\[2\sqrt {18} = 2\sqrt {{3^2} \times 2} = 2 \times 3\sqrt 2 = 6\sqrt 2 \]
So substituting into the last above expression, we get:
\[perimeter = 6\sqrt 2 + 8\sqrt 2 + 10\sqrt 2 + 6\sqrt 3 \]

Answer 28

finally, if we compute the sum amongsimilar radicals, we get:
\[perimeter = 24\sqrt 2 + 6\sqrt 3 \]

Answer 29

oh okay

Answer 30

reason i asked was my problem wanted exact answer and ratical if needed

Answer 31

ok!

Answer 32

Thank you

Answer 33

Thank you! :)