Addition and Subtraction of Surds

Q.

$\text{If}a=\frac{2-\sqrt{5}}{2+\sqrt{5}}$ and $b=\frac{2+\sqrt{5}}{2-\sqrt{5}}$, then $(a+b{)}^2=$_______.

1. 324

2. 256

3. - 18

4. 81

Q.

$\left(\frac{1}{(1-2i)}+\frac{3}{(1+i)}\right)\left(\frac{3+4i}{2-4i}\right)$is equal to

1. $\frac{1}{2}+\left(\frac{9}{2}\right)i$

2. $\frac{1}{2}-\left(\frac{9}{2}\right)i$

3. $\frac{1}{4}-\left(\frac{9}{4}\right)i$

4. $\frac{1}{4}+\left(\frac{9}{4}\right)i$

Q. Find the value of $2\sqrt{5}-4\sqrt{5}$ ?

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

Q.

If $p,q,r\in R$ and the quadratic equation $p{x}^2+qx+r=0$ has no real root, then

1. $p(p+q+r)>0$

2. $r\left(p+q+r\right)>0$

3. $q(p+q+r)>0$

4. $(p+q+r)>0$

Q.

Prove that ${\left(\frac{64}{125}\right)}^{-\frac{2}{3}}+\frac{1}{{\left(\frac{256}{625}\right)}^{\frac{1}{4}}}+\left(\frac{\sqrt{25}}{\sqrt[3]{64}}\right)=\frac{65}{16}$.

Q.

Find the roots of the following equation $\frac{1}{x+4}-\frac{1}{x-7}=\frac{11}{30}$.

Q.

If we take the sum of an irrational number and a rational number, which of the following options holds true regarding the resulting sum?

1. It may be irrational.

2. It is always irrational.

3. It is always rational.

4. It may be natural.

Q. Find the value of $2\sqrt{11}+9\sqrt{11}$ ?

1. $2\sqrt{11}$
2. $9\sqrt{11}$
3. $11\sqrt{11}$
4. $\sqrt{11}$

Q. Find the value of expression $2\sqrt{2}+\sqrt{2}$

1. $4\sqrt{2}$
2. $3\sqrt{2}$
3. $2\sqrt{2}$
4. $Noneofthese$

Q. 3$\sqrt{3}$ + 3$\sqrt{2}$ + 2$\sqrt{2}$ + 3$\sqrt{5}$ is a/an form of surd.

1. monomial
2. binomial
3. trinomial
4. quadratic

Q.

Simplify the following: $(0.001{)}^3$:

Q.

Simplify the following: $\frac{8^{\frac{1}{2}}}{8^{\frac{2}{3}}}$

Q. Simplify: $(\sqrt{75}-\sqrt{45})(\sqrt{20}+\sqrt{12})$.

Q. Simplify: $\sqrt{3}(\sqrt{5}+\sqrt{6})$.

Q. Multiply $\sqrt{7}$ by $\sqrt{5}$.

Q. Find the value of $2(\sqrt{3}{)}^6+18-4(\sqrt{3}{)}^3$ ?

1. $3\sqrt{3}(4\sqrt{3}+2)$
2. $6\sqrt{3}(2\sqrt{3}-2)$
3. $6\sqrt{3}(4\sqrt{3}-2)$
4. $6\sqrt{3}(4\sqrt{3}+2\sqrt{3})$

Q. Find sum of the following surds:
$x\sqrt{y},2x\sqrt{y},4x\sqrt{y}$.

Q. Write the rationalising factor for $2\sqrt{x}$.

Q. Find the value of $11\sqrt{7}+2\sqrt{7}-\sqrt{7}$ ?

1. $13\sqrt{7}$
2. $\sqrt{7}$
3. $7\sqrt{1}2$
4. $12\sqrt{7}$

Q. The value of $\sqrt{1+2\sqrt{1+2\sqrt{1+2+....}}}$ is

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

Q. Find the value of $2(\sqrt{3}{)}^6+18-4(\sqrt{3}{)}^3$ ?

1. $3\sqrt{3}(4\sqrt{3}+2)$
2. $6\sqrt{3}(2\sqrt{3}-2)$
3. $6\sqrt{3}(4\sqrt{3}-2)$
4. $6\sqrt{3}(4\sqrt{3}+2\sqrt{3})$

Q. What is the value obtained when we expand $({1+\sqrt{3})}^2$?

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

Q. Simplify: $(6\sqrt{2}-7\sqrt{3})(6\sqrt{2}-7\sqrt{3})$.

Q. Simplify: $\sqrt{300}-\sqrt{48}+\sqrt{75}-\sqrt{147}$.

1. $2\sqrt{3}$
2. $\sqrt{3}$
3. $4\sqrt{3}$
4. None

Q. Find sum of the following surds:
$x\sqrt{x},y\sqrt{y},3\sqrt{x^3},4\sqrt{y^3}$

Q. Find the product of $3\times \sqrt[3]{332}\times 3\times \sqrt{4}$

1. $24\sqrt[3]{34}$
2. $32\sqrt[3]{34}$
3. $36\sqrt[3]{34}$
4. $36\sqrt[3]{33}$

Q. Find the value of expression $2\sqrt{2}+\sqrt{2}$

1. $3\sqrt{2}$
2. $4\sqrt{2}$
3. $2\sqrt{2}$
4. $Noneofthese$

Q. Simplify: $4\sqrt{63}+5\sqrt{7}-8\sqrt{28}$.

Q. Find the product of $\sqrt[3]{32}$ and $\sqrt[6]{65}$.