Question

A student’s work to simplify and combine radicals is shown below. Select the statement which best applies to the sample mathematical work.
Given 4√50-2√8, I observe that √50=√20*2 and √8=√4*2, and that 25 and 4 are perfect squares, so I simplify the expression to 100√2-8√2. I can then combine these terms to get 92√2, which is my answer.

Answer 1

Your answer is incorrect. You forgot to get the square root of 25 and 4. Answer should be 16√2

we can only subtract radicals that are the same. At first glance, 4√50 - 2√8 are not the same, so they are not likely to be subtracted. However, each radical can still be simplified.

4 √50 = 4 √25 * 2 = 4 * 5 √2 = 20 √2
2 √8   = 2 √4 * 2   = 2 * 2 √2 =   4 √2

Now that the radicals are the same. then you can subtract the numbers.

20 √2 - 4 √2 = 16√2