Question

Please help me with this

Answer 1

Answer:
`9√(3)`

Work Shown:

`√(108)+√(27)\\\\√(36*3)+√(9*3)\\\\√(36)*√(3)+√(9)*√(3)\\\\6√(3)+3√(3)\\\\(6+3)√(3)\\\\9√(3)\\\\\text{Therefore,} \ √(108)+√(27) = 9√(3)\\\\`

Step-by-step explanation:

Rewrite 108 as 36*3, so that we pull out the largest perfect square factor possible. Then we use the rule
`√(A*B) = √(A)*√(B)` to break up the square root. The same idea will be used to simplify the other square root.

We can combine like terms once each individual root is simplified. If it helps, replace each
`√(3)` with x so we have 6x+3x turn into 9x. Then replace x with
`√(3)` to wrap things up.

Using a calculator,

`√(108)+√(27)\approx 15.588457\\\\`

and also

`9√(3) \approx 15.588457`

We get the same approximation to help partially confirm the answer.