Simplifying Irrational Expressions

Q. If $\frac{5\sqrt{3}+\sqrt{7}}{4\sqrt{3}-2\sqrt{7}}=X+Y\sqrt{21}$, then what is the value of $10X+10Y$.

1. $\frac{47}{10}$
2. $47$
3. $44$
4. $\frac{44}{10}$

Q. The simplest form of $\frac{\sqrt{3}}{\sqrt{2}}$ is

1. $2\sqrt{3}$
2. $\frac{6}{\sqrt{2}}$
   
3. $\frac{\sqrt{6}}{2}$
   
4. $\frac{3}{\sqrt{2}}$
   

Q. $\text{What is the simplified outcome of}\sqrt{18}+\sqrt{72}?$

1. $9\sqrt{2}$
2. $2\sqrt{9}$
3. $6\sqrt{2}$
4. None of the above

Q. Find the rational part of following expression:
$\frac{5+\sqrt{3}}{5-\sqrt{3}}$

1. $\mathrm{1.272727...}$
2. $\frac{14}{11}$
3. $1\frac{6}{22}$
4. All of the above.

Q. Evaluate the following expression:
$\frac{2+\sqrt{3}}{2-\sqrt{3}}$.

1. $7+4\sqrt{3}$
2. $7-4\sqrt{3}$
3. $7$
4. None of the above

Q. Simplified result of $\sqrt{200}-\sqrt{98}$ is

1. $3\sqrt{2}$
2. $10\sqrt{2}$
3. $7\sqrt{2}$
4. $-3\sqrt{2}$
5. (b) and (c) above.

Q. Simplified outcome of $\sqrt{72}$ is

1. $6\sqrt{2}$
2. $2\sqrt{6}$
3. $12\sqrt{6}$
4. $6\sqrt{12}$
5. None of the above

Q. $\text{Simplified result of}(\sqrt{45}+\sqrt{125})\text{is}$

1. $8\sqrt{5}$
2. $5\sqrt{5}$
3. $9\sqrt{5}$
4. $6\sqrt{5}$