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What is the following quotient? 5/ sqrt 11 - sqrt 3

What is the following quotient? 5/ sqrt 11 - sqrt 3-example-1

2 Answers

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\displaystyle\\(5)/(√(11)-√(3))=?\\\\\\\text{We rationalize the denominator.}\\\\(5)/(√(11)-√(3))=(5(√(11)+√(3)))/((√(11)-√(3))(√(11)+√(3)))=(5(√(11)+√(3)))/((11-3))=\boxed{\bf(5√(11)+5√(3)))/(8)}

User Muffe
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3 votes

Answer:

The correct option is b)
(5√(11)+5√(3))/(8)

Explanation:

We need to find the quotient of
(5)/(√(11)-√(3)),

Rationalizing the above,

By multiply and divide by conjugate of its denominator,


(5)/(√(11)-√(3)) * (√(11)+√(3))/(√(11)+√(3))


(5(√(11)+√(3)))/((√(11)-√(3))(√(11)+√(3)))

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


(5√(11)+5√(3))/((11-3))

simplify,


(5√(11)+5√(3))/(8)

Therefore, the correct option is b)
(5√(11)+5√(3))/(8)

User Siefix
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5.4k points