CLASS IX REAL NUMBERS

 If x =  $\sqrt{2}\ \ -\ 1$  then  $\frac{1}{x}$   is 

•  $\sqrt{2}\ +\ 1$  

•  $\sqrt{2}\ -\ 1$  

• 1

• 2

If a = $\sqrt{2}\ +\ 1$  then  the value of a -  $\frac{1}{a}$  is

• 2

• 1

• 0

• none of these

If x = 3 + 2  $\sqrt{2}$  then  $\sqrt{x}-\frac{1}{\sqrt{x}}$  is

• 1

• 2

• can not be found out

• none of these

 $If\frac{\sqrt{3}-1}{\sqrt{3}+1}=\ x\ +\ y\sqrt{3}$ then values of x and y are

• x = 2 , y = -1

• x = - 2 , y = -1

• x = - 1 , y = 2

• none of these

 $\sqrt{3\ -\ 2\sqrt{2}}$   is 

•  $\sqrt{2}+1$  

•  $\sqrt{2}-1$  

• 2

• 1

The simplest rationalizing factor of $\sqrt{3}+\sqrt{5}$  is

•  $\sqrt{3}+\sqrt{5}$  

•  $\sqrt{3}-\sqrt{5}$  

• 1

• none of these

 $\ \ If\ x\ =\ \frac{2}{3+\sqrt{7}}\ then\ \ \left(x\ -\ 3\right)^2\ \ \ is$  

• 1

• 4

• 7

• 10

 $If\ x\ =\ \left(2\ +\sqrt{3}\right)^{\frac{1}{3}}\ then\ x^3\ +\frac{1}{x^3}\ is$  

• 2

• 4

• 6

• 0

 $If\ \frac{5-\sqrt{3}}{2+\sqrt{3}}\ =\ x\ +y\sqrt{3}\ \ then\$  

• x = 13 , y = - 7

• x = - 13 , y = - 7

• x =  - 13 , y = 7

• x = 13 , y =  7

The seventh root of x divided by the eighth root of x is

• x

• $\sqrt{x}$

• $x^{\frac{1}{56}}$

• $\frac{1}{x^{\frac{1}{56}}}$