Simplify (2 sqrt(5) + 3 sqrt(7))^2

Question

anonymous · Answer

$$(2 \sqrt{5} + 3 \sqrt{7})^{2}$$

mrnood · Answer

(a+b)^2 = a^2 + 2ab  + b^2

expand the brackets above using that formula

mrnood · Answer

be careful of brackets - it's (2sqrt(5))^2 for example

mathstudent55 · Answer

@MrNood is doing a good job.

mathstudent55 · Answer

You can use the square of a binomial pattern he showed you, or you can just use FOIL.

mathstudent55 · Answer

You are close, but you need to be careful with the parentheses. @MrNood mentioned that too.

$(2\sqrt5)^2 + 2 \times 2\sqrt5 \times 3\sqrt7 + (3\sqrt7)^2 $

anonymous · Answer

ITS NOT CLOSED that was on accident

anonymous · Answer

I can still medal since i havent yet

mathstudent55 · Answer

Ok, now you can square the first and last terms, and multiply out the middle term.

anonymous · Answer

How do i square the first and last terms?

mathstudent55 · Answer

Square the number that multiplies the root.
Then square the root, which is just the number without the root.
Then you multiply them together.

$(2\sqrt5)^2 + 12 \sqrt{35}  + (3\sqrt7)^2$

$= 4 \times 5 + 12\sqrt{35} + 9 \times 7$

anonymous · Answer

iif i have to leave suddenly please dont leave ill be back on in like 3 minutes if it happens just stay if i do

mathstudent55 · Answer

I already had a loss of connection, and soon I need to leave.

mathstudent55 · Answer

@Darealest123

anonymous · Answer

So If you cant add it together how do you simplify, does it mean not to simplify all the way down to one number?

mathstudent55 · Answer

The answer is:

$= 20 + 12\sqrt{35} + 63$

$= 83 + 12\sqrt{35}$

That is the final answer.

anonymous · Answer

The second equation is the final answer?  i need it in steps so i can write it so im trying to figure that out

anonymous · Answer

@mathstudent55

anonymous · Answer

nvm i figured it out here is the medal thank you so much