No. √a * √b = √(a*b) only when a and b are both non-negative. Otherwise, calculate each separately, then multiply. For example: √(−9) * √(−4) = 3i * 2i = 6i^2 = −6 If both negative values are under the same square root, you multiply first, then take square root √(−9 * −4) = √(36) = 6 In this case we clearly see that √a * √b ≠ √(a*b) since a and b are negative
I don't like that solution. Doesn't the fact that sqrt(-121) appears in the original expression mean that the simplified solution must be complex, or involve a complex sub-expression somewhere? Sqrt(-121) = sqrt(121) * sqrt(-1) so sqrt(-121) = 11i so sqrt(-121)^2 = (11i)^2 = 11^2 * i^2 = -121 The solution he gives removes that when he multiplies top and bottom by -1. From what I understand, that is not valid in this case
You are partially correct. Multiplying −121 by −121 to get √(121^2) = 121 would be incorrect because the two original instances of −121 were under two separate square roots. But multiplying numerator and denominator of a fraction by −1 when they are under the same square root is allowable. Once we get the value −121/(12√5 − 29) under a common root, we can simplify as we would if we had no square root, then take the square root of the simplified expression. The way I did it was: √(−121 / (12√5 − 29)) = √(−121 (12√5 + 29) / ((12√5 − 29) (12√5 + 29))) = √(−121 (12√5 + 29) / (−121)) = √(12√5 + 29) Notice that in the last step, the −121 in the numerator and −121 in denominator cancelled out because they are located within the same square root.
bunch of unnecessary intermediate info and sheaf of spoiled papers in the first seven minutes of video and why do you constantly rewrite the condition of the problem twice at the beginning? respect the time spent by viewers, pls
Nice information
Thanks for watching! 🙏🥰💕✅
What was the need to insert(i)?121under root are both negative.Their multiplication gives 121under
root.
No. √a * √b = √(a*b) only when a and b are both non-negative.
Otherwise, calculate each separately, then multiply. For example:
√(−9) * √(−4) = 3i * 2i = 6i^2 = −6
If both negative values are under the same square root, you multiply first, then take square root
√(−9 * −4) = √(36) = 6
In this case we clearly see that √a * √b ≠ √(a*b) since a and b are negative
✓-121 x ✓-121 = -121 = - (11^2) = x
12✓5 - 29 = 2(3)(2✓5) - 9 - 20 = - (2✓5 - 3)^2 = y
✓(x/y) = 11/(2✓5 - 3) = 11(2✓5 + 3)/11 = 2✓5 + 3
I don't like that solution.
Doesn't the fact that sqrt(-121) appears in the original expression mean that the simplified solution must be complex, or involve a complex sub-expression somewhere?
Sqrt(-121) = sqrt(121) * sqrt(-1)
so sqrt(-121) = 11i
so sqrt(-121)^2 = (11i)^2 = 11^2 * i^2 = -121
The solution he gives removes that when he multiplies top and bottom by -1. From what I understand, that is not valid in this case
You are partially correct. Multiplying −121 by −121 to get √(121^2) = 121 would be incorrect because the two original instances of −121 were under two separate square roots. But multiplying numerator and denominator of a fraction by −1 when they are under the same square root is allowable. Once we get the value −121/(12√5 − 29) under a common root, we can simplify as we would if we had no square root, then take the square root of the simplified expression.
The way I did it was:
√(−121 / (12√5 − 29)) = √(−121 (12√5 + 29) / ((12√5 − 29) (12√5 + 29)))
= √(−121 (12√5 + 29) / (−121))
= √(12√5 + 29)
Notice that in the last step, the −121 in the numerator and −121 in denominator cancelled out because they are located within the same square root.
9
bunch of unnecessary intermediate info and sheaf of spoiled papers in the first seven minutes of video
and why do you constantly rewrite the condition of the problem twice at the beginning?
respect the time spent by viewers, pls