Question

Expand and simplify \5 (\10 +\2) ?

someone said the answer was 60, so i tried it and it didn’t work. can anyone help please?

Answer 1

`5√(2) +√(10)`

Explanation:

`√(5) (√(10) +√(2) ) < --Given`

`√(5) √(10) +√(5) √(2) < -- Distribute`

An equation is in its simpliest form when you eliminate as many square roots as possible. Here are some rules:

1.) You cannot combine numbers through addition or subtraction if they are under square roots. However, you can combine numbers through multiplication or division if they are under square roots.

2.) You cannot take the square root of a number if the answer is not a whole number (unless the problem says you can). However, you can solve the square root if the number can be simplfied into a "rootable?" number. In other words, the number under a square root can be divided into a number that can have its square root taken.

The first part...

`√(5) √(10) = √(5) * √(10) < --Multiply`

`√(5) * √(10) =√(50)`

`√(50) = √(25) *√(2) < --Separate`

`√(25) = 5 < --Solve`

`√(50) = 5 *√(2) < -- Substitute`

`5*√(2) =5√(2) < --Rewrite`

The second part...

`√(5) √(2) =√(5) * √(2) < -- Multiply`

`√(5) *√(2) = √(10)`

Combine both parts...

`5√(2) +√(10)`