Question

Simplify:

7 square root of 3 end root minus 4 square root of 6 end root plus square root of 48 end root minus square root of 54

Answer 1

if you mean
\[7\sqrt{3}- 4\sqrt{6} + \sqrt{48} - \sqrt{54}\] then think of it this way
\[7\sqrt{3} - 4\sqrt{6} + \sqrt{16* 3} - \sqrt{9*6}\rightarrow 7\sqrt{3} - 4\sqrt{6} + \sqrt{16}*\sqrt{3} - \sqrt{9}*\sqrt{6}\] so you get 7√3 - 4√6 + 4√3 - 3√6
and just like how you can only add x variable with x variables √3 can only be added to values with √3 and so on... so
7√3 - 4√6 + 4√3 - 3√6 =
(7√3 + 4√3) + (- 4√6 - 3√6)
11√3 - 7√6

Answer 2

is this right?

Is the simplified form of 2square root of 3 • square root of 12 rational?

Yes
No****

Answer 3

the answer is yes because
2√3 * √12=
2√3 * √4*3 =
2√3 * √4*√3=
2√3 * 2√3
and know that when numbers in ratical are same and are multiplied gets you just number
like √3 * √3 = √(3*3) = √9 = 3
so 2√3 * 2√3 = 4 * 9 = 36

Answer 4

sorry I meant 2√3 * 2√3 = 4 * 3 = 12