Roadrunner Posted January 8, 2016 Share Posted January 8, 2016 I am having a particularly obtuse morning. What are all the possible answers to square foot of 4xsquared? Quote Link to comment Share on other sites More sharing options...
regentrude Posted January 8, 2016 Share Posted January 8, 2016 What are all the possible answers to square foot of 4xsquared? Could you rephrase the question? I do not understand what you mean. Quote Link to comment Share on other sites More sharing options...
Arcadia Posted January 8, 2016 Share Posted January 8, 2016 Square roots of (4x)^2 is 4x and -4x Square roots of 4x^2 is 2x and -2x Quote Link to comment Share on other sites More sharing options...
Roadrunner Posted January 8, 2016 Author Share Posted January 8, 2016 Square roots of 4x^2 is 2x and -2x This! Thank you! Quote Link to comment Share on other sites More sharing options...
regentrude Posted January 8, 2016 Share Posted January 8, 2016 (edited) oh you mean square Root!!! I was trying to figure out what square foot could possibly mean. Edited January 8, 2016 by regentrude 1 Quote Link to comment Share on other sites More sharing options...
Roadrunner Posted January 8, 2016 Author Share Posted January 8, 2016 (edited) oh you mean square Root!!! I was trying to figure out what square foot could possibly mean. iphone is killing me! I am constantly typing what I don't mean. 😄 Edited January 8, 2016 by Roadrunner Quote Link to comment Share on other sites More sharing options...
Roadrunner Posted January 8, 2016 Author Share Posted January 8, 2016 Square roots of 4x^2 is 2x and -2x Is there a video that will walk me through this concept? I am really having a cloud in my head. Quote Link to comment Share on other sites More sharing options...
Arcadia Posted January 8, 2016 Share Posted January 8, 2016 Is there a video that will walk me through this concept? I am really having a cloud in my head. Which aspect/concept are you confused about? There is aops videos on exponents, as well as videos by Dr Edward Burger (Holt Algebra) Square root of 4x^2 = (4x^2)^(1/2) = (4^(1/2)).((x^2)^(1/2)) = (4^(1/2))x = -2x or 2x Quote Link to comment Share on other sites More sharing options...
Roadrunner Posted January 8, 2016 Author Share Posted January 8, 2016 Which aspect/concept are you confused about? There is aops videos on exponents, as well as videos by Dr Edward Burger (Holt Algebra) Square root of 4x^2 = (4x^2)^(1/2) = (4^(1/2)).((x^2)^(1/2)) = (4^(1/2))x = -2x or 2x I am confused about why it also can be negative. I get why it's 2x, but can't remember why it can also be -2x. Quote Link to comment Share on other sites More sharing options...
Arcadia Posted January 8, 2016 Share Posted January 8, 2016 (edited) I am confused about why it also can be negative. I get why it's 2x, but can't remember why it can also be -2x.(-1)(-1) = (-1)^2 = 1 which is the easy way to remember why there is a positive and negative root for a real number. ETA: Also the graph of y=x^2 is symmetrical about the y-axis. Edited January 8, 2016 by Arcadia 2 Quote Link to comment Share on other sites More sharing options...
Kathy in Richmond Posted January 8, 2016 Share Posted January 8, 2016 I am confused about why it also can be negative. I get why it's 2x, but can't remember why it can also be -2x. Actually, the square root is positive by definition! Think of the graph of the square root function. It's domain is x>=0 and its range is y>= 0. It's entirely in the first quadrant of the xy plane. So square root (4x^2) = 2 |x| (where |x| is the absolute value of x, ensuring that your answer is positive) If instead of simply finding the square root, you're now solving the equation y^2 = 4x^2, then you do get two values: (because squaring either one gets you back to 4x^2) y = +square root (4x^2) or -square root (4x^2) i.e. y = +2x or -2x For a more straightforward example: square root (5^2) = +5 square root ((-5)^2) = +5 and solving x^2 = 25 gives both x=+5 and x=-5 3 Quote Link to comment Share on other sites More sharing options...
Roadrunner Posted January 8, 2016 Author Share Posted January 8, 2016 Arcadia, Kathy, thank you!!! I get it now, and also feel like a complete idiot. â˜¹ï¸ Quote Link to comment Share on other sites More sharing options...
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