Question

What is the following quotient?


`√(6) + √(11) / √(5) + √(3)`
A.

`√(30) + 3 √(2) + √(55) + √(33) / 8`
B.

`√(30) - 3 √(2) + √(55) - √(33) / 2`
C.

`(17)/(8)`
D.

`- \frac {5}{2}`

Answer 1

Answer: The correct option is

(B)
`(√(30)+√(55)-3√(2)-√(33))/(2).`

Step-by-step explanation: We are given to find the following quotient:

`Q=(\sqrt6+√(11))/(\sqrt5+\sqrt3).`

To find the required quotient, we need to rationalize the denominator of the given expression.

We have

`Q\\\\\\=(\sqrt6+√(11))/(\sqrt5+\sqrt3)\\\\\\=((\sqrt6+√(11))(\sqrt5-\sqrt3))/((\sqrt5+\sqrt3)(\sqrt5-\sqrt3))\\\\\\=(√(30)+√(55)-√(18)-√(33))/((\sqrt5)^2-(\sqrt3)^2)\\\\\\=(√(30)+√(55)-3√(2)-√(33))/(2).`

Thus, the required co-efficient is
`(√(30)+√(55)-3√(2)-√(33))/(2).`

Option (B) is correct.

Answer 2

B) \sqrt{30} - 3 \sqrt{2} + \sqrt{55} - \sqrt{33} \div 2

Explanation:

Step 1: First we have to get rid off the roots in the denominator.

To do that, we have to multiply the numerator and the denominator by the conjugate of √5 + √3.

The conjugate of √5 + √3 is √5 - √3.

Now multiply given expression with √5 - √3

(√6 + √11) (√5 - √3)

------------- x -----------

(√5 + √3) (√5 - √3)

Step 2: Multiply the numerators and the denominators.

√6√5 - √6√3 +√11√5 -√11√3

------------------------------------------

(√5)^2 - (√3)^2

Now let's simplify to get the answer.

√30-√18 +√55 - √33

-----------------------------

5 - 3

= √30 -3√2 +√55 [√18 = √9√2 = 3√2]

--------------------------

2

The answer is \sqrt{30} - 3 \sqrt{2} + \sqrt{55} - \sqrt{33} \div 2

Thank you.