Question Text
Question 1 :
If ${n}^{k}=64$ and $n$ and $k$ are integers, which of the following cannot be a value of $n$?
Question 2 :
A computer is programmed to add $3$ to the number $N$, multiply the result by $3$, subtract $3$, and divide this result by $3$. The computer answer will be
Question 4 :
The fraction $\displaystyle \frac{2(\sqrt{2} + \sqrt{6})}{3 (\sqrt{2+ \sqrt{3}})}$ is equal to _________
Question 7 :
If $\cfrac { \sqrt { 7 } -1 }{ \sqrt { 7 } +1 } -\cfrac { \sqrt { 7 } +1 }{ \sqrt { 7 } -1 } =a+b\sqrt { 7 } $, then find the values of $a$ and $b$
Question 8 :
State whether the following statement is True or False<br>The conjugate of $x\sqrt {a} + y\sqrt {b}$ is $x\sqrt {a} - y\sqrt {b}$
Question 9 :
The conjugate of the binomial surd $\dfrac {1}{2}x + \dfrac {1}{2}\sqrt {y}$ is?
Question 10 :
State whether the following statement is True or False<br>The conjugate of $\sqrt {3} + \sqrt {2}$ is $\sqrt {2} - \sqrt {3}$
Question 11 :
If $a = \displaystyle \frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}$ and $b  = \displaystyle \frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}$, find the value $a^2+b^2-5ab$.