I'm adding 2(radical 50) + 12 (radical 8). I began by breaking the radical fifty into two parts: the radical of 25 and the radical of two. The radical of twenty five can break down into five, and the radical of two stays the way it is. Now it should read 2 5 radical of two. Do I multiply 2 and five together?
2√50 + 12√8
= 2√25√2 + 12√4√2
= 2(5)√2 + 12(2)√2
= 10√2 + 24√2
= 34√2
To simplify the expression 2√50 + 12√8, you are correct in breaking down the radicals. Let's break it down step-by-step:
Step 1: Simplify the radicals.
√50 can be simplified as follows:
√(25 × 2) = √25 × √2 = 5√2
Similarly, √8 can be simplified as follows:
√(4 × 2) = √4 × √2 = 2√2
Step 2: Substitute the simplified radicals back into the original expression.
Now we have:
2(5√2) + 12(2√2)
Step 3: Simplify further if possible.
Now, let's distribute the coefficients:
10√2 + 24√2
Step 4: Combine like terms.
Since we have the same radical (√2), we can combine the coefficients:
(10 + 24)√2 = 34√2
So, the simplified expression is 34√2.