Final answer:
To simplify 8√200 -3√162, factor out the square roots and then combine like terms, which results in the answer 53√2.
Step-by-step explanation:
To simplify 8√200 - 3√162, we need to simplify each square root separately first. The number 200 can be factored into 100 * 2, and since √100 is 10, this simplifies to 8 * 10√2 or 80√2. Similarly, 162 can be factored into 81 * 2, and √81 equals 9, so 3 * 9√2 simplifies to 27√2. Thus, we have: 8√200 - 3√162 = 80√2 - 27√2. Now, since both terms involve the square root of 2, we can combine them like terms: 80√2 - 27√2 = (80 - 27)√2 = 53√2.
So the simplified form of 8√200 - 3√162 is 53√2. To simplify the expression 8√200 -3√162, we need to simplify each radical term separately. The square root of 200 can be written as √(100*2), which is equal to 10√2. The square root of 162 can be written as √(81*2), which is equal to 9√2. Substituting these values back into the expression, we get 8(10√2) - 3(9√2).This simplifies to 80√2 - 27√2, which further simplifies to 53√2. Therefore, the simplified expression is 53√2.