Multiplication of Surds

Q.

Simplify the following expression $\left(\sqrt{5}-\sqrt{2}\right)\left(\sqrt{5}+\sqrt{2}\right)$

Q.

Rationalize the denominator of $\frac{1}{2-\sqrt{3}}$

1. 4 + √3

2. 3 + 2√3

3. 2 + 2√3

4. 2 + √3

Q. If $x=\frac{\sqrt{3}+1}{2},$ find the value of $4x^3+2x^2-8x+7$.

1. $0$
2. $100$
3. $11$
4. $10$

Q.

If $x^p{y}^q={(x+y)}^{p+q}$, then $\frac{dy}{dx}=$

1. $\frac{y}{x}$

2. $\frac{-y}{x}$

3. $\frac{x}{y}$

4. $-\frac{x}{y}$

Q.

$\text{If}m=\frac{1}{3-2\sqrt{2}}\text{then,}{m}^2=$ _______.

1. $34$

2. $17-12\sqrt{2}$

3. $24\sqrt{2}$

4. $17+12\sqrt{2}$

Q. Find the value of $0.\overline{13}+0.\overline{12}$.

Q.

The term independent of $x$ in the expansion of ${\left[\frac{x+1}{x^{{\displaystyle \raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}-x^{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}+1}-\frac{x-1}{x-x^{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}}\right]}^{10}$, $x\ne 1$, is equal to

Q.

If $\frac{2\sqrt{7}+3\sqrt{5}}{\sqrt{7}+\sqrt{5}}=P\sqrt{35}+Q$, then what Is The value of $2P+Q$.

Q.

Question 2 (i)
Simplify $(3+\sqrt{3})(2+\sqrt{2})$ .

Q. Find an irrational number between $\frac{2}{7}$ and $\frac{3}{7}$.

Q.

The value of given expression is $6+{\log }_{\frac{3}{2}}\left(\frac{1}{3\sqrt{2}}\sqrt{4-\frac{1}{3\sqrt{2}}\sqrt{4-\frac{1}{3\sqrt{2}}.....}}\right)$

1. $4$

2. $5$

3. $7$

4. None of these

Q. Evaluate: $\sqrt{5}+2\sqrt{6}+\sqrt{8}-2\sqrt{15}$.

Q.

Let $S$ be the set of all complex numbers $z$ satisfying $\left|z-2+i\right|\ge 5$. If the complex number $z_0$ is such that $\frac{1}{z_0-1}$ is the maximum of the set $\left\{\frac{1}{z-1};z\in S\right\}$

then the principle argument of $\frac{4-z_0-\overline{z_0}}{z_0-\overline{z_0}+2i}$

1. $\frac{\mathrm{\pi }}{4}$

2. $-\frac{\mathrm{\pi }}{2}$

3. $\frac{3\mathrm{\pi }}{4}$

4. $\frac{\mathrm{\pi }}{2}$

Q. Simplify :
$3\sqrt{3}+2\sqrt{27}+\frac{7}{\sqrt{3}}$.

Q. If $x=9+4\sqrt{5},$ then the value of $\sqrt{x}-\frac{1}{\sqrt{x}}$ is ____.

Q. Classify the following number as rational or irrational:
$(\sqrt{2}-2{)}^2$.

Q. Prove that $\sqrt{2}$ is irrational number.

Q.

Find the missing fractions:

$\frac{9}{11}-\square =\frac{6}{11}$

Q. Find the square roots of following surds :
$5+2\sqrt{6}$.

Q. Find the square root in the form of binomial surd:
$55-14\sqrt{6}$.

Q. Simplify: $(3\sqrt{5}-5\sqrt{2})(4\sqrt{5}+3\sqrt{2})$.

Q. Find the square root in the form of binomial surd:
$8+\sqrt{63}$.

Q. Given that $\sqrt{3}=1.732$, then the value of $\sqrt{75}+\frac{1}{2}\sqrt{48}-\sqrt{192}$$=-1.732$.

1. True
2. False

Q. If $x=\frac{5-\sqrt{21}}{2}$, then $(x^2+\frac{1}{x^2})-(x+\frac{1}{x})=$?

1. $21$
2. $18$
3. $4$
4. $5$

Q. Find an irrational number between $\frac{2}{7}$ and $\frac{3}{7}$.

Q. Find the square root of following surds:
$9+2\sqrt{14}$.

Q.

$\left(X-2\right)\left(X-3\right)\left(X+4\right)$ Multiply using expansion.

Q.

${14}^{\frac{1}{7}}\times {14}^{\frac{1}{7}}$ can be represented as ___________.

1. 
   (${14}^2{)}^{\frac{1}{7}}$

2. ($14\times 14{)}^{\frac{1}{7}}$

3. ${14}^{\frac{1}{7}+\frac{1}{7}}$

4. All of the above

Q.

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

1. 3

2. 1

3. 6

4. 4

Q.

Find the value of $(\sqrt{2}+\sqrt{2})(\sqrt{2}-\sqrt{2})$.

1. 1

2. 2
3. 3
4. 0