Question

find the perimeter of a rectangle whose sides are (5-sqrt 18) and (4+3 sqrt 18)

Answer 1

perimeter = length + length + width + width

Answer 2

the square root numbers is what is getting me confused

Answer 3

\(\bf length = 5-\sqrt{18}\qquad width=4+3\sqrt{18}
\\ \quad \\
perimeter =(5-\sqrt{18})+(5-\sqrt{18})+(4+3\sqrt{18})+(4+3\sqrt{18})
\\ \quad \\
perimeter = 2(5-\sqrt{18})+2(4+3\sqrt{18})\qquad distributing
\\ \quad \\
perimeter = 10-2\sqrt{18}+8+6\sqrt{18}\implies 10+8+6\sqrt{18}-2\sqrt{18}\)

Answer 4

so i dont need to simplify the square roots

Answer 5

keep in mind that, when the radical and radicand are the same, you can just add them like like terms, thus -> \(\bf +6\sqrt{18}-2\sqrt{18}\implies +4\sqrt{18}\)

Answer 6

yes.... once you sum them up, you can simplify them, yes \(\bf {\color{blue}{ 18\implies 3\cdot 3\cdot 2\implies 3^2\cdot 2}}
\\ \quad \\ \quad \\

4\sqrt{18}\implies 4\sqrt{3^2\cdot 2}\implies 4\cdot 3\sqrt{2}\)

Answer 7

my final answer would be [18+ 4 ^{3} \sqrt{2}\]

Answer 8

ahemm is 4 * 3... no 4^3 ...

Answer 9

what do you mean ? exactly

Answer 10

\(\bf 4\sqrt{18}\implies 4\sqrt{3^2\cdot 2}\implies 4\cdot 3\sqrt{2}\implies 12\sqrt{2}\)

if the number inside the root, has an exponent that matches the root
then the number comes out, without its exponent

Answer 11

\(\bf 4\sqrt{18}\implies {\Large 4\sqrt[{\color{red}{ 2}}]{3^{\color{red}{ 2}}\cdot 2}}\implies 4\cdot 3\sqrt{2}\implies 12\sqrt{2}\)

Answer 12

okay, i think i got it..thank youu !!!

Answer 13

yw