Solve Simple Square Roots: (-6)^1/2 x (-7)^1/2 = (42)^1/2

  • Thread starter Thread starter frozen7
  • Start date Start date
AI Thread Summary
The discussion revolves around the calculation of the expression ((-6)^1/2) x ((-7)^1/2) and its relation to (42)^1/2. The error identified is in applying the property x^z y^z = (xy)^z, which is only valid for positive values of x and y. The correct interpretation shows that the product of the square roots of negative numbers introduces an imaginary unit, leading to the conclusion that the expression equals -(42)^1/2 rather than (42)^1/2. The participants emphasize the importance of handling negative square roots correctly in mathematical operations. Understanding these principles is crucial for accurate calculations involving complex numbers.
frozen7
Messages
163
Reaction score
0
((-6)^ 1/2 ) ( (-7)^1/2) = (42)^1/2

((-6)^ 1/2 ) ( (-7)^1/2) = (6^ 1/2 ) ( 7^1/2) ( i ^2)
= -(42)^1/2

Can anyone tell me where I did wrong?
 
Physics news on Phys.org
frozen7 said:
((-6)^ 1/2 ) ( (-7)^1/2) = (42)^1/2

((-6)^ 1/2 ) ( (-7)^1/2) = (6^ 1/2 ) ( 7^1/2) ( i ^2)
= -(42)^1/2

Can anyone tell me where I did wrong?
((-6)^ 1/2 ) ( (-7)^1/2) = (42)^1/2
this step
x^zy^z=(xy)^z
is not true in general only when x,y>0
 
((-6)(-7))^(1/2)=(42)^(1/2)
(42)^(1/2)=(42)^(1/2)
should have left the right hand side alone
 
Thanks a lot..
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

Are the 2nd and 3rd problems in this video correctly solved? (charged dipole and organ pipe problems)
Replies
3
Views
1K
LASER Applications help please
Replies
4
Views
685
Derive ## a^{7}\equiv a\pmod {42} ## for all ## a ##
Replies
6
Views
2K
How to solve this problem in sinusoidal motion? (Satellite orbiting the Earth)
Replies
5
Views
654
Show that ## 168=3\cdot 7\cdot 8 ## divides ## a^{6}-1 ##
Replies
4
Views
2K
Analyse motion of an oscillator: x(t)=0.2cos(12*pi*t)
Replies
5
Views
1K
Energy of particle in simple harmonic motion
Replies
13
Views
1K
To find the tipping point of a lamina
Replies
2
Views
1K
To find the distance of a horizontally suspended rod from a ceiling
Replies
2
Views
1K
8.01 MIT OCW PS1.4: Throw and Catch (Kinematics)
Replies
4
Views
1K

Hot Threads

Recent Insights

Back
Top