In math we're doing a review sheet and i don't get any of it so can someone please help!!
What is the simplest form of the expression Radical 28 + radical 175 - radical 7
holy moly no need to post this 20 times :P
so the problem is you can't add or subtract radicals that aren't the same, so you have to modify them so that you have the same numbers inside the radicals
the easiest way to visualize this sort of thing is to break all the numbers down to their primes
28=7*2*2
175=5*5*7
7=7
(to do this easily just keep dividing by larger primes until you can't anymore, starting with 2, then 3,5,7 etc)
so root(7*2*2)+root(5*5*7)-root(7)
now when you have numbers multiplying each other inside a radical like that, you can rewrite it like this
root(7)*root(2*2)+root(7)*root(5*5)-root(7)
and when the same number multiplies itself inside a root like root(2*2) it just cancels the root. (i.e. 2*2 is 4 and the square root of 4 is 2)
so now we have 2*root(7)+5*root(7)-root(7)
now all the roots are the same so you can add them and subtract them easily.
if this is hard to imagine, just pretend that root(7)=x such that
2x+5x-x
or 6x
but x=root(7)
so 6*root(7) the answer!
hope this helps
To simplify the expression Radical 28 + Radical 175 - Radical 7, we need to simplify each radical separately and then combine the simplified terms.
Let's start with Radical 28. To simplify it, we need to find the largest perfect square that goes into 28. In this case, the largest perfect square that divides 28 is 4, since 4 * 7 = 28. Therefore, we can write Radical 28 as 2 * Radical 7.
Next, let's simplify Radical 175. Similarly, we need to find the largest perfect square that divides 175. The largest perfect square is 25 since 25 * 7 = 175. We can then write Radical 175 as 5 * Radical 7.
Now, let's simplify Radical 7. Since 7 is a prime number, it does not have any perfect square factors. Therefore, Radical 7 cannot be simplified any further.
Now that we have simplified each term, we can combine them. The expression becomes 2 * Radical 7 + 5 * Radical 7 - Radical 7.
Since all the terms have Radical 7, we can combine them by adding the coefficients: (2 + 5 - 1) * Radical 7.
Simplifying, we get 6 * Radical 7.
Therefore, the simplest form of the expression Radical 28 + Radical 175 - Radical 7 is 6 * Radical 7.