Surd Quiz
Q1. $\sqrt{3+2\sqrt{2}}=?$
1. $1+\sqrt{2}$
2. $-(1+\sqrt{2})$
3. $\pm (2+\sqrt{1})$
4. $-(2+\sqrt{1})$
5. $2+\sqrt{1}$
Q2. $\sqrt{2\sqrt{2\sqrt{2\sqrt{2\sqrt{2 \cdots}}}}}=?$
1. $2$
2. $5$
3. $\sqrt{2}$
4. $1$
Q3. $\sqrt{6+\sqrt{6+\sqrt{6+\sqrt{6+\sqrt{6+ \cdots}}}}}=?$
1. $4$
2. $\sqrt{6}$
3. $3$
4. $\sqrt{3}$
5. None of these
Q4. $2-\frac{1}{2-\frac{1}{2-\frac{1}{2 \cdots}}}=?$
1. $-1$
2. $1$
3. $4$
4. $2$
5. $\frac{1}{2}$
Q5. $\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}+\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}$
1. $2$
2. $10$
3. $6$
4. $8$
5. $\sqrt{6}$
Q6. $\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+2}+\frac{1}{2+\sqrt{5}}+\frac{1}{\sqrt{5}+\sqrt{6}}+\cdots +\frac{1}{\sqrt{99}+10}=?$
1. $20$
2. $10+\sqrt{2}$
3. $10-\sqrt{2}$
4. $23$
Q7. $\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}-\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}$
1. $\sqrt{6}$
2. $2\sqrt{6}$
3. $3\sqrt{6}$
4. $4\sqrt{6}$
Q8. $\frac{\sqrt{3}+\sqrt{2}}{\sqrt{7}+\sqrt{5}}$ (sym) $\frac{\sqrt{7}-\sqrt{5}}{\sqrt{3}-\sqrt{2}}$, (sym)=?
1. $\geq$
2. $\leq$
3. $<$
4. $=$
5. $>$
Q9. $\sqrt{2}$, $\sqrt[3]{5},\sqrt[4]{7},\sqrt[5]{11}$ which is bigger?
1.$\sqrt{2}$
2. $\sqrt[3]{5}$
3. $\sqrt[4]{7}$
4. $\sqrt[5]{11}$
Q10. If $\sqrt{3}-\sqrt{2}=x$, then what is the value of $\sqrt{6}$
1. $x^2$
2. $\sqrt{x}$
3. $\frac{1}{4}(x^2+\frac{1}{x^2})$
4. $\frac{1}{4}(x^2-\frac{1}{x^2})$