Question

Can someone explain this process? https://i.imgur.com/OMlMK9J.png

Answer 1

(2r)^2 means (2r)*(2r) or 2*r*2*r or 2*2*r*r

Answer 2

3^2 is 3*3 or 9
3^2 + 3^2 is 2*3^2 or 2*9

Answer 3

so you have
\[ 2\cdot 2 \cdot r \cdot r = 2 \cdot 9 \]
or write 2*2 as 4 and r*r as r^2
\[ 4 r^2 = 2 \cdot 9 \]

Answer 4

Alright, great that makes sense, what's the deal with last part tho? How does 9/2 turn to 3*root(2) over 2? @ phi

Answer 5

after dividing both sides by 4 you get
\[ \frac{4}{4} r^2 = \frac{2}{4} \cdot 9 \]
or
\[ r^2 = \frac{9}{2} \]
take the square root of both sides
\[ \sqrt{r^2} = \sqrt{\frac{9}{2}} \\ r= \frac{\sqrt{9}}{\sqrt{2}}\\
r= \frac{3}{\sqrt{2}}
\]

Answer 6

people don't usually show division by a square root (I think back before calculators, people found it too hard to figure out)

multiply top and bottom by sqr(2)