Simplify.
3 square root2(5square root 2 - 6 square root 12)
3√2(5√2 - 6√12)
= 15(2) - 18√24
= 30 - 18√4√6
= 30 - 36√6
i have one more that is a bit different
2 square root 2(5 square root 10- 3 square root 2)
100+23
To simplify the expression 3√2(5√2 - 6√12), we can start by simplifying the terms within the parentheses.
√2 can be simplified further if we can find a perfect square within it. Since 2 = 2 × 1, we can rewrite it as √(2 × 1) = √2 × √1 = √2.
Similarly, √12 can be simplified. We know that 12 = 4 × 3, so we can rewrite it as √(4 × 3) = √4 × √3 = 2√3.
Now let's substitute these simplified terms back into the expression:
3√2(5√2 - 6√12)
= 3√2(5√2 - 6(2√3))
Next, we can distribute the 3√2 to each term inside the parentheses:
= 3√2 × 5√2 - 3√2 × 6(2√3)
= 3 × 5 × √2 × √2 - 3 × 6 × 2 × √2 × √3
= 15 × 2 - 36 × 2√3
Now we can simplify further:
= 30 - 72√3
So, the simplified expression is 30 - 72√3.