Answer : $2(\sqrt[3]{5})$

Answer : $\large\frac{610}{33}$

Answer : rational number

Answer : $\large\frac{104}{275}$

$\large\frac{5+2\sqrt 3}{7+4\sqrt 3}$$=a+b\sqrt 3$$\large\frac{5+2\sqrt 3}{7+4\sqrt 3}$ $\times $$\l...

$x= \frac {\sqrt3 +1}{2} \;\; \implies 2x = \sqrt3 + 1\;\; (or)\;\; 2x - 1 = \sqrt3$Squaring on bot...

Answer : $\sqrt[5]{a^3b^2c}$

Answer : $6\sqrt 7+\large\frac{3}{2}$$\sqrt {6}$

Answer : 3$\large\frac{1}{1+\sqrt 2}\times \large\frac{\sqrt 2-1}{\sqrt 2-1}=\frac{\sqrt 2-1}{1}$$=\...

$x=\sqrt{\large\frac{5+2\sqrt 6}{5-2\sqrt 6}}$$ x^2 = \frac {5+ 2\sqrt6}{5-2\sqrt6}$$ x =\sqrt {\Lar...

$a=2+\sqrt 3$$ \large\frac {1}{a} = \large\frac {1}{2 + \sqrt3} \times \large\frac {2-\sqrt3}{2-\sqr...

Answer : $\large\frac{33}{2}$

$x=\large\frac{\sqrt 5+\sqrt 3}{\sqrt 5-\sqrt 3}$ and $y=\large\frac{\sqrt 5-\sqrt 3}{\sqrt 5+\sqrt ...

$\large\frac{\sqrt 3-1}{\sqrt 3+1}=$$a-b\sqrt 3$$\frac {\sqrt3 - 1}{\sqrt3 + 1} \times \frac {\sqrt3...

$ x + \sqrt15 = 4 \;\;\; \implies x = 4 - \sqrt15$$\begin {align*}\frac {1}{x} &= \frac {1}{4-\s...

Answer : $\sqrt 3+\sqrt 2$

$\sqrt{14-b\sqrt{3}}=\sqrt 8+\sqrt 6$Squaring on both sides:$ 14 - b\sqrt3 = (\sqrt8)^2 + (\sqrt6)^2...

Solution : $x= 3 -2 \sqrt 2$$\large\frac{1}{x}=\frac{1}{3- 2 \sqrt 2} \times \large\frac{3+2 \sqrt 2...

$x = 2 + \sqrt3$$\begin{align*}\frac{1}{x}& = \frac{1}{2+\sqrt3} = 2 \\ &= \frac{1}{2+\sqrt...

Solution : $x= 2 +\sqrt 3$=> $(x-2)=\sqrt 3$=> $x^2-4x+4=3$=> $x^2-4x+1=0$$x^3-2x^2-7x+5=x(...

Solution : $a^2+ab+b^2= (a+b)^2-ab$$a+b= \large\frac{\sqrt{2}+1}{\sqrt{2}-1}+\large\frac{\sqrt{2}-1}...

$\sqrt{13-a\sqrt{10}}=\sqrt8+\sqrt 5$Squaring on both sides:$13- a\sqrt10 = 8 + 5 +2\sqrt10$$13 - a\...

Answer : 2

Answer : 4

Answer : 500

Answer : 36

$HCF \times LCM$ =Product of numbers$a \times 18=36 \times 2$$a=\large\frac{36 \times 2}{18}$$\quad=...

Solution : $HCF \times LCM$ = Product of numbers$13 \times LCM = 26 \times 169$$\therefore LCM =\la...

Solution : LCM of 35,56 and 91 is $35= 5\times 7$ $56= 2 \times 2 \times 2 \times 7$$91= 7 \times 13...

$LCM = 180 ; HCF = 6$$\begin{align*}30 \times x &= 180 \times 6 \\ \implies x & =\frac{1...

LCM $\times$ HCF = Product of two numbers$\therefore LCM = \frac{306 \times 657}{9} = 22338$

Answer : non-terminating repeating

$\large\frac{13}{3125} = \frac{13}{(5)^5}$Hence it is a terminating decimal

Answer : 19https://clay6.com/mpaimg/a4.jpgHence the HCF is 19

Answer : non-terminating,repeating

Yes. It is True eg. $6\times 7\times 8$ is divisible by 6

Answer : both $p$ and $q$ are prime positive numbers

Answer : $0 < y < x$

Answer : any prime positive

Squares of coprime number are also coprimeAnswer = coprime

$P_1^2 - P_2^2 = (P_1 + P_2)(P_1-P_2)$Sum of two odd number is an even number. Any number multiplied...

Sum of two irrational number is an irrational number. (eg.) $\sqrt7 +\sqrt3$ = an irrational number....

Whenever an integer is multiplied by 2, it becomes an even number.Hence it is a FALSE statement.

Answer : no value of $n$

$\begin{align*}9^{2n}-4^{2n} &= (9^n)^2 - (4^n)^2 \\ &= (9^n +4^n)(9^n-4^n) \end{align*}$He...

Since 3 is the least prime factor, a is an odd number. Similarly 7 is the least prime factor implies...

Answer : any real number

$a-d+a+a+d = 15$$\begin{align*}\implies3a & = 15 \\ a&=5\end{align*}$$\begin{align*}(a-d)(a)...

Let the three parts be a - d, a, a + da - d + a + a + d = 24$\implies 3a = 24 $ $\implies$ a = 8$\be...

$\begin{align*}\text{amount to be paid }& = Rs 12,000 - 6,000 \\ & = Rs6,000\end{align*}$$\b...