Multiply and express in simplest radical form: left parenthesis, 6, plus, 3, square root of, 75, end square root, right parenthesis, left parenthesis, 5, plus, square root of, 3, end square root, right parenthesis (6+3 75 ​ )(5+ 3 ​ )

Answer 1

First, let's simplify the expressions inside the parentheses:

6 + 3√75 = 6 + 3√(25 * 3) = 6 + 15√3

5 + √3 = 5 + √3

Now, multiply the two expressions:

(6 + 15√3)(5 + √3)
= 6(5) + 6(√3) + 15√3(5) + 15√3(√3)
= 30 + 6√3 + 75√3 + 15(3)
= 30 + 6√3 + 75√3 + 45
= 75 + 81√3

Therefore, the expression (6+3√75)(5+√3) simplifies to 75 + 81√3.