She just PROVED that you do not need absolute value because x cannot be negative when square rooting x^3. So if x can only be positive you do not need absolute value. You don’t need it because it can only be positive. You can’t square root a negative number. When it comes to square root of x^3, you only need absolute value if there is another variable with an odd exponent inside the radical. If you already know a number could only be positive and be impossible to be negative, that’s why you don’t need absolute value there.
In the first example √2x^3 , can't I assume that x ≥ 0? If x < 0, then x^3 < 0 and we can't take a square root of a negative number in the real number system. Also in the final answer, |x|√2x , the same situation occurs. Thank you.
I believe you are correct. It's so hard to find anyone to explain this concept completely. If you're still looking for a comprehensive explanation, check out this guy's video... It's the only one I've found that seems to explain it completely... ruclips.net/video/PH3I8wOt1Zc/видео.html
the assumption that x>=0 is only for the real number system. Once you learn imaginary numbers (usually in Algebra 2), then her explanation is correct. Notice how her explanation includes how negatives inside the radical come out as i.
@@davidriddell315 No. actually she just proved that you don’t need absolute value. She just proved that x cannot be negative. It can only be positive when squaring x^3. Therefore you do not need absolute value. If x can only be positive, then there’s no need to put absolute value because you already know it’s positive.
So, a square root function is defined for x greater than or equal to zero. I understand what both David and Simba are saying, but I think that the problem should specify whether x is all real numbers or complex numbers.
This person isn’t using absolute value correctly. If the power inside the even root is odd then you already know that the variable must be positive for the problem to exist. Therefore, absolute value is unnecessary.
Over the set of complex numbers, you do not already know that the variable must be positive for the problem to exist. You CAN take even roots of negative numbers. Therefore, you need absolute value as she explains.
@@davidriddell315 No. she just proved you don’t need absolute value because it’s not possible for x to be negative. That’s the whole argument. You don’t need absolute value to square root a x^3 because you cannot square root a negative number. She just proved that to be true. X cannot be a negative. She just proved it. So if x cannot be negative, it can only be positive; therefore you do not need absolute value to square root x^3. Only time you need absolute value to square root x^3 is if there is another variable with an odd exponent inside the radical.
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seriously just saved me so much more frustration, the way the stupid program I use was explaining it made no damn sense at all, thank you
It helped a lot!!
She just PROVED that you do not need absolute value because x cannot be negative when square rooting x^3. So if x can only be positive you do not need absolute value. You don’t need it because it can only be positive. You can’t square root a negative number. When it comes to square root of x^3, you only need absolute value if there is another variable with an odd exponent inside the radical. If you already know a number could only be positive and be impossible to be negative, that’s why you don’t need absolute value there.
Thank you maam for an excellent explanation on abs. val used when working with radicals.
In the first example √2x^3 , can't I assume that x ≥ 0? If x < 0, then x^3 < 0 and we can't take a square root of a negative number in the real number system. Also in the final answer, |x|√2x , the same situation occurs. Thank you.
I believe you are correct. It's so hard to find anyone to explain this concept completely. If you're still looking for a comprehensive explanation, check out this guy's video... It's the only one I've found that seems to explain it completely...
ruclips.net/video/PH3I8wOt1Zc/видео.html
the assumption that x>=0 is only for the real number system. Once you learn imaginary numbers (usually in Algebra 2), then her explanation is correct. Notice how her explanation includes how negatives inside the radical come out as i.
@@davidriddell315 No. actually she just proved that you don’t need absolute value. She just proved that x cannot be negative. It can only be positive when squaring x^3. Therefore you do not need absolute value. If x can only be positive, then there’s no need to put absolute value because you already know it’s positive.
So, a square root function is defined for x greater than or equal to zero. I understand what both David and Simba are saying, but I think that the problem should specify whether x is all real numbers or complex numbers.
This person isn’t using absolute value correctly. If the power inside the even root is odd then you already know that the variable must be positive for the problem to exist. Therefore, absolute value is unnecessary.
i was thinking the same thing!
Over the set of complex numbers, you do not already know that the variable must be positive for the problem to exist. You CAN take even roots of negative numbers. Therefore, you need absolute value as she explains.
@@davidriddell315 No. she just proved you don’t need absolute value because it’s not possible for x to be negative. That’s the whole argument. You don’t need absolute value to square root a x^3 because you cannot square root a negative number. She just proved that to be true. X cannot be a negative. She just proved it. So if x cannot be negative, it can only be positive; therefore you do not need absolute value to square root x^3. Only time you need absolute value to square root x^3 is if there is another variable with an odd exponent inside the radical.