Simplify (3 sqrt 8 + 4 sqrt 9)^2.
3,600
(3√8 + 4√9)^2
= (3√8 + 12)^2
= 72 + 72√8 + 144
= 216 + 72(2√2)
= 216 + 144√2 or appr 419.65
Please note that I did not post 3,600. An impersonator, aka Anonymous, from Corvallis, Oregon, posted it.
To simplify the expression (3√8 + 4√9)^2, you can follow these steps:
Step 1: Expand the square of a binomial. Use the formula (a + b)^2 = a^2 + 2ab + b^2.
Step 2: Substitute the values of a and b with the given terms.
Step 3: Simplify any square roots that can be simplified.
Let's apply these steps:
Step 1: Expand the square.
(3√8 + 4√9)^2 = (3√8)^2 + 2 * (3√8 * 4√9) + (4√9)^2
Step 2: Simplify the squares.
= (3^2 * (√8)^2) + 2 * (3√8 * 4√9) + (4^2 * (√9)^2)
= 9 * 8 + 2 * 3 * 4 * √(8 * 9) + 16 * 9
Step 3: Simplify the square root and perform the multiplications.
= 72 + 24√72 + 144
= 72 + 144 + 24√(8 * 9)
= 216 + 24√72
Therefore, the simplified form of (3√8 + 4√9)^2 is 216 + 24√72.