+0  
 
0
198
1
avatar+644 

If  \(z = \frac{ \left\{ \sqrt{3} \right\}^2 - 2 \left\{ \sqrt{2} \right\}^2 }{ \left\{ \sqrt{3} \right\} - 2 \left\{ \sqrt{2} \right\} }\)find z.

waffles  Mar 15, 2018
 #1
avatar
0

 

((sqrt(3))^2 - 2 (sqrt(2))^2)/(sqrt(3) - 2 sqrt(2))=z

 

Multiply exponents. (sqrt(2))^2 = 2^(2/2):

((sqrt(3))^2 - 22^(2/2))/(sqrt(3) - 2 sqrt(2))

 

((sqrt(3))^2 - 2×2)/(sqrt(3) - 2 sqrt(2))

 

Cancel exponents. (sqrt(3))^2 = 3:

(3 - 2×2)/(sqrt(3) - 2 sqrt(2))

 

(-4 + 3)/(sqrt(3) - 2 sqrt(2))

 

(-1)/(sqrt(3) - 2 sqrt(2))

 

Multiply numerator and denominator of (-1)/(sqrt(3) - 2 sqrt(2)) by -1:

1/(2 sqrt(2) - sqrt(3))

 

Multiply numerator and denominator of 1/(2 sqrt(2) - sqrt(3)) by 2 sqrt(2) + sqrt(3):

(2 sqrt(2) + sqrt(3))/((2 sqrt(2) - sqrt(3)) (2 sqrt(2) + sqrt(3)))

 

(2 sqrt(2) - sqrt(3)) (2 sqrt(2) + sqrt(3)) = 2 sqrt(2)×2 sqrt(2) + 2 sqrt(2) sqrt(3) - sqrt(3)×2 sqrt(2) - sqrt(3) sqrt(3) = 8 + 2 sqrt(6) - 2 sqrt(6) - 3 = 5:

 

z = (2sqrt(2) + sqrt(3)) / 5

Guest Mar 15, 2018

20 Online Users

avatar
avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.