<p>I have question on this
V= square root ok?</p>
<p>V(2x+20)= x-2</p>
<p>When I solve there are two solutions 8 and -2. I need to substitute in to check them right?
With x= 8:
V(2*8+20)= 8-2
V36=6 (correct)</p>
<p>But with x =-2:
V[2<em>(-2)+20]= (-2)</em>2
V16= -4
The book says it doesnt work.
But why can't the square root of 16 equals to -4???</p>
<p>Are you serious right now?</p>
<p>The square root of sixteen is 4.
Does 4 = -4?</p>
<p>The square root of sixteen can both be 4 and -4
?</p>
<p>@SandwichGirl
He has a very valid question. And what you said is kinda stupid.</p>
<p>@belly
The square root of a number x is defined to be the number r which satisfies r^2 = x. For any non-zero real number (including negative numbers), there are TWO roots. 16 has roots 4 and -4, because (4)^2 = (-4)^2 = 16.</p>
<p>Your mistake here is that the notation Vx refers to the non-negative (principal) square root of x. It’s just a convention. So, while both 4 and -4 are square roots of 16, V16 can only be 4.</p>
<p>V(2x+20)= x-2</p>
<p>which means (2x+20)^1/2
square each side to isolate 2x+20.</p>
<p>2x+20 = (x-2)^2
2x+20 = x^2-4x+4
0 = x^2 -6x -16
0 = (x+2)(x-8)
x = -2, 8</p>
<p>Check:</p>
<p>V(2(-2)+20)= -2-2
V(-4+20)= -4
V(16)=-4
+/-4 = -4
YES </p>
<p>-4 IS a square root of 16. Square -4. What is it? 16. Thus it is a square root. Same for the bottom check.</p>
<p>V(2(8)+20)= 8-2
V(16+20)=6
V36=6
+/-6 = 6
YES</p>
<p>^ V16 = 4. The square root of 16 can be either 4 or -4. But V16 does not mean ‘square root of 16’ (it refers to the PRINCIPAL, or non-negative, square root of 16). V16 cannot be negative.</p>
<p>If you were to graph V(2x + 20), you (or, at least, most people who have done this in algebra) would not graph anything below the x-axis. The graph would be strictly non-negative. This is for the same reason; because Vx represents the non-negative root of x.</p>
<p>…I can’t believe I’m getting this worked up over an Algebra question.</p>
<p>no homework help questions allowed…</p>
<p>
Are you serious right now…?</p>
<p>@OP</p>
<p>Sorry about the comment; I guess my A in Algebra 2 didn’t really mean anything.</p>
<p>When you see Square root, it is implied that they are only looking for the positive square root. That’s all you need to know</p>
<p>^Stick to making sandwiches :D</p>
<p>Always consider both roots in algebra…</p>
<p>You guys… whenever you see the radical sign √ (V in this case), it’s referring to the positive root of whatever number you’re rooting. </p>
<p>y² = 16</p>
<p>now y = +/- 4, but the √y² has to equal l y l (abs. value). The radical = “the positive square root” in English. It just is. It’s a vocabulary/semantic thing. That’s what it’s referring to.</p>
<p>@sandwich girl: lol I have an A too but my school doesn’t teach me anything that’s why I’m going over some of the problem in the summer
@porkperson: This is not homework
Your answer does make sense, estrat. However, I would like to see this written on a website. Anyone found one yet?</p>
<p>Did the problem limit you only to principal square roots?</p>
<p>it doesn’t say anything</p>
<p>The only time I ever paid attention to principal square roots was when I was instructed to, which only occurred rarely.</p>
<p>Nonetheless, the equations is true if and only if you consider the principal square root. -2 doesn’t work, so 8 is the only answer.</p>