+0  
 
0
50
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!

Guest Feb 2, 2018
Sort: 

2+0 Answers

 #1
avatar
+1

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)

Guest Feb 2, 2018
 #2
avatar
+1

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)

Guest Feb 2, 2018

4 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details