Square root /w fraction and exponent: how to simplilfy correctly

Quasimoto

New member
Joined
Jun 13, 2019
Messages
11
Dear forum users,


I've been trying to figure this out.
15604635019921445585783.jpg

Could someone explain to me how this is the answer?

15604637110941456507112.jpg

Thank you in advance!
 
[math]\left(\dfrac{2\sqrt{3}}{3\sqrt{2}}\right)^{3} = \left(\dfrac{2}{3}\right)^{3}\cdot\left(\dfrac{\sqrt{3}}{\sqrt{2}}\right)^{3} = \left(\dfrac{2}{3}\right)^{3}\cdot\left(\dfrac{\sqrt{3}}{\sqrt{2}}\right)^{2}\cdot\left(\dfrac{\sqrt{3}}{\sqrt{2}}\right)[/math]
Follow?
 
1st expression = ~.5443
2nd expression = ~2.0528
As noted by the expansion that tkhunny is using the "solution" given in the OP is incorrect. The actual answer has a \(\displaystyle \sqrt{2}\) in the denominator. The fraction in front of the radicals is wrong as well.

Is this the solution to a different problem?

-Dan
 
I
[math]\left(\dfrac{2\sqrt{3}}{3\sqrt{2}}\right)^{3} = \left(\dfrac{2}{3}\right)^{3}\cdot\left(\dfrac{\sqrt{3}}{\sqrt{2}}\right)^{3} = \left(\dfrac{2}{3}\right)^{3}\cdot\left(\dfrac{\sqrt{3}}{\sqrt{2}}\right)^{2}\cdot\left(\dfrac{\sqrt{3}}{\sqrt{2}}\right)[/math]
Follow?

I am following it yes.
 
As noted by the expansion that tkhunny is using the "solution" given in the OP is incorrect. The actual answer has a \(\displaystyle \sqrt{2}\) in the denominator. The fraction in front of the radicals is wrong as well.

Is this the solution to a different problem?

-Dan
I looked for the answer again and yes the solution is to a different problem.
But my original answer is still wrong.
So I will be trying to figure it out later today.

Thank you
 
Dear forum users, I've been trying to figure this out.
You posted two images:
\(\displaystyle \boxed{\left(\dfrac{2\sqrt3}{3\sqrt2}\right)^3}\) & \(\displaystyle \boxed{\frac{32}{27}\sqrt3}\)
The second image is not the reduction of the first.
You tell us at what step you fail to understand.
1) \(\displaystyle \frac{2\sqrt3}{3\sqrt2}=\frac{2\sqrt3\cdot\sqrt2}{3\sqrt2\cdot\sqrt2}\)
2) \(\displaystyle \frac{2\sqrt3}{3\sqrt2}=\frac{2\sqrt6}{3\cdot 2}\)
3) \(\displaystyle \frac{2\sqrt3}{3\sqrt2}=\frac{\sqrt6}{3}\)

4) \(\displaystyle \left(\frac{\sqrt6}{3}\right)^3=\frac{6\sqrt6}{27}\)
5) \(\displaystyle \boxed{\left(\frac{\sqrt6}{3}\right)^3=\frac{2\sqrt6}{9}}\) CLICK HERE
 
You posted two images:
\(\displaystyle \boxed{\left(\dfrac{2\sqrt3}{3\sqrt2}\right)^3}\) & \(\displaystyle \boxed{\frac{32}{27}\sqrt3}\)
The second image is not the reduction of the first.
You tell us at what step you fail to understand.
1) \(\displaystyle \frac{2\sqrt3}{3\sqrt2}=\frac{2\sqrt3\cdot\sqrt2}{3\sqrt2\cdot\sqrt2}\)
2) \(\displaystyle \frac{2\sqrt3}{3\sqrt2}=\frac{2\sqrt6}{3\cdot 2}\)
3) \(\displaystyle \frac{2\sqrt3}{3\sqrt2}=\frac{\sqrt6}{3}\)

4) \(\displaystyle \left(\frac{\sqrt6}{3}\right)^3=\frac{6\sqrt6}{27}\)
5) \(\displaystyle \boxed{\left(\frac{\sqrt6}{3}\right)^3=\frac{2\sqrt6}{9}}\) CLICK HERE
The second image is indeed the wrong solution to the problem.
Thank you for explaining step by step.

I failed at step 4, I used the exponent at the beginning instead of solving everything what is inside of the parentheses.

Thank you very much I appreciate the time and effort.
 
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