Conjugate Pair

Q. The conjugate of the surd 2 - 3√5 is _______.

1. 2√5 - 3
2. -2√5 - 3
3. -$\sqrt{2}$ + 3√5
4. 2 + 3√5

Q.

find product of 3 - √7 an its conjugate

Q.

If a and b are rational numbers, find 'a' and 'b' when

$\frac{\sqrt{7}-2}{\sqrt{7}+2}=a\sqrt{7}+b$

1. $a=-\frac{4}{3},b=\frac{-11}{3}$

2. $a=\frac{-4}{3},b=\frac{11}{3}$

3. $a=\frac{4}{3},b=\frac{-11}{3}$

4. $a=\frac{4}{3},b=\frac{11}{3}$

Q.

Find the square of $\frac{2\sqrt{5}}{5}$

1. $\frac{3}{5}$

2. $\frac{2}{5}$

3. $\frac{4}{5}$

4. $\frac{1}{5}$

Q. Which of the following should be multiplied with $\sqrt{3}+\sqrt{2}$ to get a rational number?

1. $\sqrt{3}-\sqrt{2}$
2. $-\sqrt{3}+\sqrt{2}$
3. $\sqrt{3}+\sqrt{2}$
4. $3+\sqrt{2}$

Q. Which of the following is the conjugate surd of $-3-\sqrt{8}$?

1. $-\sqrt{3}-\sqrt{8}$
2. $\sqrt{3}-\sqrt{8}$
3. $-3+\sqrt{8}$
4. $3+2\sqrt{8}$

Q.

The conjugate of the surd 2√15 - 3√5 is

1. 

2. 

3. 

4. 

Q. If y & z are two complex numbers such that |y|=|z| and arg y=arg z then show that y & z are conjugate complex numbers. Also, if |y|=|z|=1 and arg y=arg z then show that y=1/z.

Q.

Rationalising $\frac{\sqrt{2}+\sqrt{3}}{\sqrt{3}-\sqrt{2}}$ will give __________.

1. $5-2\sqrt{6}$

2. $5+2\sqrt{6}$

3. $7+2\sqrt{6}$

4. $7-2\sqrt{6}$

Q. $(1+\sqrt{2})+(1-\sqrt{2})=$

1. 1
2. 2
3. 3

Q. $(2+\sqrt{3}{)}^2+(2-\sqrt{3}{)}^2=$

1. 7
2. 5
3. 14
4. 12

Q. If $\sqrt{13-a\sqrt{10}}=\sqrt{8}+\sqrt{5}$ then $a=$

Q. Express the following with rational denominator:

$\left(vi\right)\frac{\sqrt{3}+1}{2\sqrt{2}-\sqrt{3}}$

Q.

The rationalising factor for the number $3-7\sqrt{2}$ is

1. $3+2\sqrt{7}$

2. $-3-2\sqrt{7}$

3. $3+7\sqrt{2}$

4. $-3+7\sqrt{2}$

Q. $\mathrm{Fill}\mathrm{in}\mathrm{the}\mathrm{blank}\mathrm{with}\mathrm{the}\mathrm{correct}\mathrm{sign}.\mathrm{The}\mathrm{conjugate}\mathrm{of}1+\sqrt{2}\mathrm{is}1$ $\sqrt{2}.$

1. $+$
2. $-$

Q.

The conjugate of the surd 2√15 - 3√5 is

1. 

2. 

3. 

4. 

Q. Which of the following is the conjugate surd of $-3-\sqrt{8}$?

1. $-\sqrt{3}-\sqrt{8}$
2. $\sqrt{3}-\sqrt{8}$
3. $-3+\sqrt{8}$
4. $3+2\sqrt{8}$

Q. $(\sqrt{4}+\sqrt{3})\times (\sqrt{4}-\sqrt{3})=$

1. 1
2. 2
3. 7
4. 3

Q. The result of $(3+\sqrt{5})\times$, is a rational number.

1. $\sqrt{5}$
2. 3
3. $(3+\sqrt{5})$
4. $(3-\sqrt{5})$

Q. The conjugate of $3-\sqrt{5+x}$ is $3+\sqrt{5+x}$. Verify