Question

Simplify - 1/root3+root2 - 2/root5-root3 - 3/root2- root5 Answer = 2root2

Answer 1

Answer:

Step-by-step explanation:

The given equation is:

$-\frac{1}{\sqrt{3}+\sqrt{2}}-2\frac{1}{\sqrt{5}-\sqrt{2}}-3\frac{1}{\sqrt{2}-\sqrt{5}}$

On rationalising the above given expression, we get

$-\frac{(\sqrt{3}-\sqrt{2})}{3-2}-2\frac{(\sqrt{5}+\sqrt{3})}{5-3}-3\frac{(\sqrt{2}+\sqrt{5})}{2-5}$

=$-\sqrt{3}+\sqrt{2}-\sqrt{5}+\sqrt{3}+\sqrt{2}+\sqrt{5}$

=$2\sqrt{2}$

which is the required answer

Answer 2

"To determine: The value of  $-\frac { 1 }{ \sqrt { 3 } +\sqrt { 2 }} -\frac { 2 }{ \sqrt { 5 } -\sqrt { 3 }} -\frac { 3 }{ \sqrt { 2 } -\sqrt { 5 }}$

Calculation:

Step 1: Take the conjugate of each denominator of each fraction and multiply the conjugate with the corresponding numerator and denominator for each fraction

$-\frac { 1 }{ \sqrt { 3 } +\sqrt { 2 }} \times \frac { \sqrt { 3 } -\sqrt { 2 }}{ \sqrt { 3 } -\sqrt { 2 }} -\frac { 2 }{ \sqrt { 5 } -\sqrt { 3 }} \times \frac { \sqrt { 5 } +\sqrt { 3 }}{ \sqrt { 5 } +\sqrt { 3 }} -\frac { 3 }{ \sqrt { 2 } -\sqrt { 5 }} \times \frac { \sqrt { 2 } +\sqrt { 5 }}{ \sqrt { 2 } +\sqrt { 5 }}$

Step 2: Simplifying the above equation we get

$-\frac { \sqrt { 3 } -\sqrt { 2 }}{ 3-2 } -\frac { 2(\sqrt { 5 } +\sqrt { 3 } )}{ 5-3} -\frac { 3(\sqrt { 2 } +\sqrt { 5 } )}{ 2-5 }$

$= -\frac { \sqrt { 3 } -\sqrt { 2 }}{ 1 } -\frac { 2(\sqrt { 5 } +\sqrt { 3 } )}{ 2 } -\frac { 3(\sqrt { 2 } +\sqrt { 5 } )}{ -3 }$

Step 3: Cancelling the factors from the numerators and denominators, we get

$-(\sqrt { 3 } -\sqrt { 2 } )-(\sqrt { 5 } +\sqrt { 3 } )+(\sqrt { 2 } +\sqrt { 5 } )$

Step 4: Removing the parentheses, we get

$-\sqrt { 3 } +\sqrt { 2 } -\sqrt { 5 } -\sqrt { 3 } +\sqrt { 2 } +\sqrt { 5 } =2\sqrt { 2 }$"