Question

What is the following quotient?

Answer 1

Answer:

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

Step-by-step 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.

Answer 2

Answer:  The correct option is

(B) $\dfrac{\sqrt{30}+\sqrt{55}-3\sqrt{2}-\sqrt{33}}{2}.$

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

$Q=\dfrac{\sqrt6+\sqrt{11}}{\sqrt5+\sqrt3}.$

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

We have

$Q\\\\\\=\dfrac{\sqrt6+\sqrt{11}}{\sqrt5+\sqrt3}\\\\\\=\dfrac{(\sqrt6+\sqrt{11})(\sqrt5-\sqrt3)}{(\sqrt5+\sqrt3)(\sqrt5-\sqrt3)}\\\\\\=\dfrac{\sqrt{30}+\sqrt{55}-\sqrt{18}-\sqrt{33}}{(\sqrt5)^2-(\sqrt3)^2}\\\\\\=\dfrac{\sqrt{30}+\sqrt{55}-3\sqrt{2}-\sqrt{33}}{2}.$

Thus, the required co-efficient is $\dfrac{\sqrt{30}+\sqrt{55}-3\sqrt{2}-\sqrt{33}}{2}.$

Option (B) is correct.