+0  
 
-1
612
2
avatar

1.Simplify $\frac{6}{2\sqrt 3 - 3}$ as much as possible.

2.Simplify $\dfrac{1}{\sqrt2-1}+\dfrac{1}{\sqrt2+1}$ as much as possible.

3.Simplify $\frac{2\sqrt[3]9}{1 + \sqrt[3]3 + \sqrt[3]9}.$

Thank you in advance!

 Feb 2, 2018
 #1
avatar
0

2.

 

Simplify the following:

1/(sqrt(2) - 1) + 1/(sqrt(2) + 1)

 

Multiply numerator and denominator of 1/(sqrt(2) - 1) by the conjugate of the denominator.

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

(sqrt(2) + 1)/((sqrt(2) - 1) (sqrt(2) + 1)) + 1/(sqrt(2) + 1)

 

Multiply sqrt(2) - 1 and 1 + sqrt(2) together using FOIL.

(sqrt(2) - 1) (sqrt(2) + 1) = -1 - sqrt(2) + sqrt(2)×1 + sqrt(2) sqrt(2) = -1 - sqrt(2) + sqrt(2) + 2 = 1:

(sqrt(2) + 1)/1 + 1/(sqrt(2) + 1)

 

Look for one in the denominator of sqrt(2) + 1.

(sqrt(2) + 1)/1 = sqrt(2) + 1:

sqrt(2) + 1 + 1/(sqrt(2) + 1)

 

Multiply numerator and denominator of 1/(sqrt(2) + 1) by the conjugate of the denominator.

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

1 + sqrt(2) + (sqrt(2) - 1)/((sqrt(2) + 1) (sqrt(2) - 1))

 

Multiply 1 + sqrt(2) and sqrt(2) - 1 together using FOIL.

(sqrt(2) + 1) (sqrt(2) - 1) = -1 + 1 sqrt(2) - sqrt(2) + sqrt(2) sqrt(2) = -1 + sqrt(2) - sqrt(2) + 2 = 1:

1 + sqrt(2) + (sqrt(2) - 1)/1

Look for one in the denominator of sqrt(2) - 1.

(sqrt(2) - 1)/1 = sqrt(2) - 1:

1 + sqrt(2) + sqrt(2) - 1

 

Evaluate 1 + sqrt(2) - 1 + sqrt(2).

1 + sqrt(2) - 1 + sqrt(2) = 2 sqrt(2):

2 sqrt(2)

 Feb 2, 2018
 #2
avatar
0

1.

 

Simplify the following:

6/(2 sqrt(3) - 3)

 

Multiply numerator and denominator of 6/(2 sqrt(3) - 3) by the conjugate of the denominator.

Multiply numerator and denominator of 6/(2 sqrt(3) - 3) by 2 sqrt(3) + 3:

(6 (2 sqrt(3) + 3))/((2 sqrt(3) - 3) (2 sqrt(3) + 3))

 

Multiply 2 sqrt(3) - 3 and 3 + 2 sqrt(3) together using FOIL.

(2 sqrt(3) - 3) (2 sqrt(3) + 3) = -3×3 - 3×2 sqrt(3) + 2 sqrt(3)×3 + 2 sqrt(3)×2 sqrt(3) = -9 - 6 sqrt(3) + 6 sqrt(3) + 12 = 3:

(6 (2 sqrt(3) + 3))/3

 

In (6 (2 sqrt(3) + 3))/3, divide 6 in the numerator by 3 in the denominator.

6/3 = (3×2)/3 = 2:

2 (2 sqrt(3) + 3)

 Feb 2, 2018

16 Online Users

avatar
avatar
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.