Respuesta :
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.[tex][/tex]
Answer: The correct option is
(B) [tex]\dfrac{\sqrt{30}+\sqrt{55}-3\sqrt{2}-\sqrt{33}}{2}.[/tex]
Step-by-step explanation: We are given to find the following quotient:
[tex]Q=\dfrac{\sqrt6+\sqrt{11}}{\sqrt5+\sqrt3}.[/tex]
To find the required quotient, we need to rationalize the denominator of the given expression.
We have
[tex]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}.[/tex]
Thus, the required co-efficient is [tex]\dfrac{\sqrt{30}+\sqrt{55}-3\sqrt{2}-\sqrt{33}}{2}.[/tex]
Option (B) is correct.
