Question

Simplify (2 {sqrt 5}+ 3 {sqrt 7})^2. Show your work. Justify each step.

Thanks in advance for the help!!!

Answer 1

Is this your question ?
\[(2\sqrt 5 + 3\sqrt 7)^2\]

Answer 2

yes

Answer 3

Let's use the idenitity,
\[(a+b)^2=a^2+2ab+b^2\]
here
\[a=2\sqrt 5\]
\[b=3\sqrt 7\]
Can you try ?

Answer 4

How do I plug that into the equation? I'm very confused....

Answer 5

\[(2\sqrt 5+3 \sqrt 7)^2=\]
\[(2\sqrt 5)^2+2\times(2\sqrt 5)\times(3\sqrt 7)+(3\sqrt 7)^2\]

Can you try now?

Answer 6

Thank you very much for you help!
Do I multiply the 2by both 2 and 5 (the part after the first plus sign)? I think I understand how to do the rest of it.

Answer 7

Only one
\[2\times 2\times \sqrt5 \times 3\times \sqrt 7=2\times 2\times 3 \times \sqrt 5\times \sqrt 7 \]
\[=12\times \sqrt 5\times \sqrt 7\]
There you go \(\uparrow\)

Answer 8

Thank you!! You've been very helpful :)

Answer 9

Welcome :)