Explanation for Question 19 From the Math (No Calc) Section on the 2017 May Sat
Question 19 asks us for the value of our, 2 and they give us this equation right here. 3 So what we want to do is get all the RS on one side, 4 isolate for R and that's how we solve our first step is going to 5 be to get rid of, of this cube root. 6 And we do that by taking both sides to 7 the third power. So taking everything to the third power, 8 we do it to the left side that actually just cancels out and we're 9 left with nine R minus two. And when we do it to the left 10 side to the right side, we have to make sure that we have parentheses 11 around our terms because the cube doesn't just apply to the R. 12 It also applies to the one-half. So when we go ahead 13 and cube everything, we got one over eight, 14 because one times, one times, one is one, 15 two times, two times two is eight are cubed. 16 Now we want to kind of simplify on both sides. 17 I think the easiest way to do this is to multiply both sides by 18 eight, that gets rid of this. 19 And then here we can kind of multiply that and see how that simplifies. 20 We do eight times nine. Um, 21 we get 72 and a little 22 bit easy actually to do that is divided eight by two first, 23 we got four. So now we'll just do four times nine, 24 which is 36 36 are equals are cute. 25 Now I all the RS on one side. So to get rid of the, 26 on the left side, we divide by our, and we're left with 36 equals 27 R squared to get rid of the squared. 28 We take the square root of both sides and we get six equals 29 R. And that is our answer.