00:01
So the first problem here with the question three, we're going to solve using order of operations.
00:06
So order of operations says that we're going to start with our grouping symbols or the parentheses.
00:10
Simplify that first.
00:11
Then do exponents, multiplying, dividing, adding, and subtracting.
00:16
So what i see here is i've got a set of parentheses, and this square root here is almost like a grouping symbol.
00:21
So we're going to look inside these first to evaluate.
00:24
So inside the square root, i have 5 squared minus 4 squared.
00:28
Well, 5 squared is 25 and 4 squared is 16.
00:33
So it's 25 minus 16.
00:35
Inside the parentheses here, i have 5 minus 4, which is 1.
00:40
From there, i'm going to take care of what's inside the grouping symbol of the square root.
00:45
So 25 minus 16 is 9.
00:47
So this is the square root of 9 plus 7 times 1 squared.
00:53
Now, the square root of 9 is like an exponent.
00:56
The square to 9 is 3.
00:57
1 squared is 1, so it's 7 times 1.
01:02
From there, i can multiply 7 times 1 to get 7, and then 3 plus 7 to get 10.
01:08
And this is our final answer.
01:11
Now let's move on to the next one.
01:14
So when you're doing this at the order of operations here, we look at the decimals and we take care of that.
01:20
So i have 7 .5, and i subtract 8 .4.
01:24
So i have 1 plus 7 .5 minus 8 .4.
01:28
Is negative 0 .9, all over 9 .6.
01:33
I'm then going to divide that by 9 .6, because division would be next.
01:39
So this becomes 1 plus a negative 0 .09375.
01:47
So then from there, i can subtract or add 1 plus negative 0 .09375.
01:54
And our final answer here is 0 .906.
01:59
90625.
02:01
For the next one, we're going to take care of the stuff in the grouping singles first.
02:05
So i have in here a 1 .8 minus 4 .3.
02:09
That's the first thing i'm going to do is subtract.
02:12
1 .8 minus 4 .3 is negative 2 .5.
02:17
Then the square root is almost like a grouping symbol.
02:20
So i'm going to combine 15 and 10 together to get 25.
02:24
Now, this absolute value bars around here tells us we need to make that value positive.
02:30
So negative 2 .5 becomes a positive 2 .5 because it represents distance.
02:37
The square root of 5 is next, and we take the square root of that to get 5.
02:42
So what we have is 0 .4 times 5.
02:47
Next comes multiplying, so we're to multiply 5 times 0 .4, and that gets us 2.
02:54
Now 2 .5 plus 2 is our last piece to get 4 .5.
02:59
So the next one here, we're going to go to the parentheses inside the grouping symbols, inside the grouping symbols.
03:05
The very first thing we need to take care of is this 3 minus 8.
03:08
So 3 minus 8 is negative 5.
03:11
So i have negative 5 squared minus 4 minus i'm going to go ahead and do that 3 minus 8 here as well to get negative 5.
03:19
Now that we have that, we're going to go ahead and square because the exponents would be next inside this pair of grouping symbols.
03:24
So negative 5 squared is 25.
03:27
So i have 25 minus 4 here and then minus the negative 5.
03:32
Next step, i still have stuff going on in the grouping simple, so i'm going to subtract those.
03:37
25 minus 4 is 21.
03:40
Then i'm going to subtract a negative 5.
03:42
This is a double negative.
03:44
So that becomes a plus sign.
03:46
And our final answer here is 26.
03:48
So these would be the answers for the first question dealing with a, b, c, and d...