# Help with math

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I am having a particularly obtuse morning. What are all the possible answers to square foot of 4xsquared?

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What are all the possible answers to square foot of 4xsquared?

Could you rephrase the question? I do not understand what you mean.

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Square roots of (4x)^2 is 4x and -4x

Square roots of 4x^2 is 2x and -2x

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Square roots of 4x^2 is 2x and -2x

This! Thank you!

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oh you mean square Root!!! I was trying to figure out what square foot could possibly mean.

Edited by regentrude
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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. ðŸ˜„

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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.

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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

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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.

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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.

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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

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I get it now, and also feel like a complete idiot. â˜¹ï¸

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