body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

Pearson Algebra 2 Common Core, 2011

PA

Pearson Algebra 2 Common Core, 2011 View details

End-of-Course Assessment

Finish the assignment

Exercise 5 Page 964

To rationalize a fraction with a binomial denominator, multiply the numerator and denominator of the fraction by the conjugate of the denominator.

D

Practice makes perfect

We want to find a simpler form of the given fraction with a binomial denominator. To do it, we will rationalize the fraction by multiplying the numerator and denominator of the fraction by the conjugate of the denominator. We find the conjugate by changing the sign of the second term of the expression.

Binomial	Conjugate
a + b	a - b
a - b	a + b

In this case, the conjugate of the denominator is 3+sqrt(2).

sqrt(5)/3-sqrt(2)

a/b=a * (3+sqrt(2))/b * (3+sqrt(2))

sqrt(5)(3+sqrt(2))/(3-sqrt(2))(3+sqrt(2))

(a-b)(a+b)=a^2-b^2

sqrt(5)(3+sqrt(2))/9-(sqrt(2))^2

( sqrt(a) )^2 = a

sqrt(5)(3+sqrt(2))/9-2

Subtract term

sqrt(5)(3+sqrt(2))/7

Distribute sqrt(5)

3sqrt(5)+sqrt(2)sqrt(5)/7

sqrt(a)*sqrt(b)=sqrt(a* b)

3sqrt(5)+sqrt(2* 5)/7

Multiply

3sqrt(5)+sqrt(10)/7

This corresponds to option D.

Subchapter links

Exercises p.964-971