Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
125901	Find the Vertex Form	g(x)=-3x^2+24x-41	$g (x) = - 3 x^{2} + 24 x - 41$
125902	Find the Vertex Form	f(x)=x^2-6x-24	$f (x) = x^{2} - 6 x - 24$
125903	Find the Vertex Form	p(x)=x^2-4x-2	$p (x) = x^{2} - 4 x - 2$
125904	Find the Vertex Form	P(x)=-5x^2+15x	$P (x) = - 5 x^{2} + 15 x$
125905	Rationalize the Denominator	-5/(3 square root of 5-2)	$\frac{- 5}{3 \sqrt{5} - 2}$
125906	Rationalize the Denominator	5/(3 square root of 5)	$\frac{5}{3 \sqrt{5}}$
125907	Find the Symmetry	x^2-y^3=19	$x^{2} - y^{3} = 19$
125908	Find the Symmetry	xy^2+12=0	$x y^{2} + 12 = 0$
125909	Find the Symmetry	x-y^2=-2	$x - y^{2} = - 2$
125910	Rationalize the Denominator	12/( square root of 5)	$\frac{12}{\sqrt{5}}$
125911	Rationalize the Denominator	11/( square root of 33x)	$\frac{11}{\sqrt{33 x}}$
125912	Rationalize the Denominator	11/(3+ square root of 19)	$\frac{11}{3 + \sqrt{19}}$
125913	Rationalize the Denominator	10/(3 square root of 5)	$\frac{10}{3 \sqrt{5}}$
125914	Rationalize the Denominator	( square root of 5x^6)/( square root of 2x^4y^3)	$\frac{\sqrt{5 x^{6}}}{\sqrt{2 x^{4} y^{3}}}$
125915	Rationalize the Denominator	( square root of 2x^6)/( square root of 5x^4y^5)	$\frac{\sqrt{2 x^{6}}}{\sqrt{5 x^{4} y^{5}}}$
125916	Rationalize the Denominator	(1- square root of 6)/(6 square root of 7- square root of 42)	$\frac{1 - \sqrt{6}}{6 \sqrt{7} - \sqrt{42}}$
125917	Rationalize the Denominator	(3+ square root of 8)/(3- square root of 8)	$\frac{3 + \sqrt{8}}{3 - \sqrt{8}}$
125918	Rationalize the Denominator	4/(7- square root of 2)	$\frac{4}{7 - \sqrt{2}}$
125919	Rationalize the Denominator	(4 square root of 3)/(3 square root of 2)	$\frac{4 \sqrt{3}}{3 \sqrt{2}}$
125920	Rationalize the Denominator	(3 square root of 3)/( square root of 5)	$\frac{3 \sqrt{3}}{\sqrt{5}}$
125921	Rationalize the Denominator	(p-81)/( square root of p+9)	$\frac{p - 81}{\sqrt{p} + 9}$
125922	Rationalize the Denominator	9/( square root of 3x)	$\frac{9}{\sqrt{3 x}}$
125923	Rationalize the Denominator	-9/(3 square root of 3-2)	$\frac{- 9}{3 \sqrt{3} - 2}$
125924	Rationalize the Denominator	9/( square root of 11)	$\frac{9}{\sqrt{11}}$
125925	Rationalize the Denominator	square root of (7x)/27	$\sqrt{\frac{7 x}{27}}$
125926	Rationalize the Denominator	cube root of 5/16	$\sqrt[3]{\frac{5}{16}}$
125927	Rationalize the Denominator	7/( square root of 21x)	$\frac{7}{\sqrt{21 x}}$
125928	Rationalize the Denominator	(7 square root of 2)/( square root of 5)	$\frac{7 \sqrt{2}}{\sqrt{5}}$
125929	Rationalize the Denominator	(7 square root of 7)/( square root of 5)	$\frac{7 \sqrt{7}}{\sqrt{5}}$
125930	Rationalize the Denominator	17/(3+ square root of 11)	$\frac{17}{3 + \sqrt{11}}$
125931	Rationalize the Denominator	2/(3- square root of 7)	$\frac{2}{3 - \sqrt{7}}$
125932	Rationalize the Denominator	2/(7- square root of 2)	$\frac{2}{7 - \sqrt{2}}$
125933	Rationalize the Denominator	2/(9- square root of 2)	$\frac{2}{9 - \sqrt{2}}$
125934	Rationalize the Denominator	(2- square root of 7)/(2+ square root of 7)	$\frac{2 - \sqrt{7}}{2 + \sqrt{7}}$
125935	Rationalize the Denominator	(5 square root of 3)/(4 square root of 2)	$\frac{5 \sqrt{3}}{4 \sqrt{2}}$
125936	Rationalize the Denominator	(5 square root of 5)/( square root of 2)	$\frac{5 \sqrt{5}}{\sqrt{2}}$
125937	Rationalize the Denominator	6/( square root of 8)	$\frac{6}{\sqrt{8}}$
125938	Rationalize the Denominator	1/( cube root of cd)	$\frac{1}{\sqrt[3]{c d}}$
125939	Rationalize the Denominator	fourth root of 16/(9x^5)	$\sqrt[4]{\frac{16}{9 x^{5}}}$
125940	Rationalize the Denominator	9/( square root of 5+ square root of 3)	$\frac{9}{\sqrt{5} + \sqrt{3}}$
125941	Rationalize the Denominator	7/(4- square root of 5)	$\frac{7}{4 - \sqrt{5}}$
125942	Rationalize the Denominator	( square root of 5-2)/( square root of 5+2)	$\frac{\sqrt{5} - 2}{\sqrt{5} + 2}$
125943	Rationalize the Denominator	( square root of 7- square root of 2)/( square root of 14- square root of 13)	$\frac{\sqrt{7} - \sqrt{2}}{\sqrt{14} - \sqrt{13}}$
125944	Rationalize the Denominator	( square root of 8)/( square root of xy)	$\frac{\sqrt{8}}{\sqrt{x y}}$
125945	Find the Behavior (Leading Coefficient Test)	f(x)=5x^8-2x^7-8x^6+1	$f (x) = 5 x^{8} - 2 x^{7} - 8 x^{6} + 1$
125946	Find the Behavior (Leading Coefficient Test)	f(x)=-12x^3+36x+x^5	$f (x) = - 12 x^{3} + 36 x + x^{5}$
125947	Find the Symmetry	y=x^4-2x^2	$y = x^{4} - 2 x^{2}$
125948	Find the Symmetry	y=3- square root of x	$y = 3 - \sqrt{x}$
125949	Find the Symmetry	2x^4+7=y^2	$2 x^{4} + 7 = y^{2}$
125950	Find the Symmetry	x=y^2+19	$x = y^{2} + 19$
125951	Find the Symmetry	x=y^2+15	$x = y^{2} + 15$
125952	Find the Symmetry	x^2-y^3=14	$x^{2} - y^{3} = 14$
125953	Find the Symmetry	x^2-y^3=10	$x^{2} - y^{3} = 10$
125954	Find the Symmetry	6y=5x^2-7	$6 y = 5 x^{2} - 7$
125955	Find the Symmetry	x-y^2=14	$x - y^{2} = 14$
125956	Find the Symmetry	xy-x^2=3	$x y - x^{2} = 3$
125957	Find the Symmetry	x=y^4-y^2+3	$x = y^{4} - y^{2} + 3$
125958	Rationalize the Denominator	5/(2+ square root of 13)	$\frac{5}{2 + \sqrt{13}}$
125959	Rationalize the Denominator	5/( square root of 6x)	$\frac{5}{\sqrt{6 x}}$
125960	Rationalize the Denominator	5/( square root of 12)	$\frac{5}{\sqrt{12}}$
125961	Rationalize the Denominator	5/(6+3 square root of 2)	$\frac{5}{6 + 3 \sqrt{2}}$
125962	Rationalize the Denominator	5/(6- square root of 2)	$\frac{5}{6 - \sqrt{2}}$
125963	Rationalize the Denominator	5/(4 square root of 2-1)	$\frac{5}{4 \sqrt{2} - 1}$
125964	Rationalize the Denominator	5/(8-4 square root of 2)	$\frac{5}{8 - 4 \sqrt{2}}$
125965	Rationalize the Denominator	6/(2- square root of 3)	$\frac{6}{2 - \sqrt{3}}$
125966	Rationalize the Denominator	6/(3- square root of 2)	$\frac{6}{3 - \sqrt{2}}$
125967	Rationalize the Denominator	6/(3- square root of 5)	$\frac{6}{3 - \sqrt{5}}$
125968	Rationalize the Denominator	( square root of 11- square root of 7)/( square root of 11+ square root of 7)	$\frac{\sqrt{11} - \sqrt{7}}{\sqrt{11} + \sqrt{7}}$
125969	Rationalize the Denominator	( square root of 11)/(2- square root of 5)	$\frac{\sqrt{11}}{2 - \sqrt{5}}$
125970	Rationalize the Denominator	( square root of -1)/((3+8i)-(2+5i))	$\frac{\sqrt{- 1}}{(3 + 8 i) - (2 + 5 i)}$
125971	Rationalize the Denominator	( cube root of 7a)/( cube root of 2c)	$\frac{\sqrt[3]{7 a}}{\sqrt[3]{2 c}}$
125972	Rationalize the Denominator	( square root of 7w)/( square root of 5)	$\frac{\sqrt{7 w}}{\sqrt{5}}$
125973	Rationalize the Denominator	( square root of 7)/( square root of 5x)	$\frac{\sqrt{7}}{\sqrt{5 x}}$
125974	Rationalize the Denominator	( square root of a+1)/(2 square root of a- square root of b)	$\frac{\sqrt{a} + 1}{2 \sqrt{a} - \sqrt{b}}$
125975	Rationalize the Denominator	( square root of 5x^4)/( square root of 3x^2y^5)	$\frac{\sqrt{5 x^{4}}}{\sqrt{3 x^{2} y^{5}}}$
125976	Rationalize the Denominator	7/(2 square root of 5-1)	$\frac{7}{2 \sqrt{5} - 1}$
125977	Rationalize the Denominator	7/(3- square root of 11)	$\frac{7}{3 - \sqrt{11}}$
125978	Rationalize the Denominator	8/(4- square root of 5)	$\frac{8}{4 - \sqrt{5}}$
125979	Rationalize the Denominator	(8i)/(-4-4i)	$\frac{8 i}{- 4 - 4 i}$
125980	Rationalize the Denominator	( square root of 3x^4)/( square root of 2x^2y^3)	$\frac{\sqrt{3 x^{4}}}{\sqrt{2 x^{2} y^{3}}}$
125981	Rationalize the Denominator	square root of 14/6	$\sqrt{\frac{14}{6}}$
125982	Rationalize the Denominator	fourth root of 16/(9x)	$\sqrt[4]{\frac{16}{9 x}}$
125983	Rationalize the Denominator	fourth root of 3/4	$\sqrt[4]{\frac{3}{4}}$
125984	Rationalize the Denominator	square root of 10/14	$\sqrt{\frac{10}{14}}$
125985	Rationalize the Denominator	13/(5+ square root of 31)	$\frac{13}{5 + \sqrt{31}}$
125986	Rationalize the Denominator	(15 square root of 7)/(7 square root of 5)	$\frac{15 \sqrt{7}}{7 \sqrt{5}}$
125987	Rationalize the Denominator	y/( square root of 2+ square root of y)	$\frac{y}{\sqrt{2} + \sqrt{y}}$
125988	Rationalize the Denominator	x/( square root of 11- square root of 6)	$\frac{x}{\sqrt{11} - \sqrt{6}}$
125989	Rationalize the Denominator	x/( square root of 13- square root of 10)	$\frac{x}{\sqrt{13} - \sqrt{10}}$
125990	Rationalize the Denominator	(p-100)/( square root of p+10)	$\frac{p - 100}{\sqrt{p} + 10}$
125991	Rationalize the Denominator	x/( square root of 7- square root of 5)	$\frac{x}{\sqrt{7} - \sqrt{5}}$
125992	Rationalize the Denominator	(10 square root of 2)/(2 square root of 5- square root of 3)	$\frac{10 \sqrt{2}}{2 \sqrt{5} - \sqrt{3}}$
125993	Rationalize the Denominator	11/(3+ square root of 13)	$\frac{11}{3 + \sqrt{13}}$
125994	Rationalize the Denominator	(10 square root of 7)/(7 square root of 5)	$\frac{10 \sqrt{7}}{7 \sqrt{5}}$
125995	Rationalize the Denominator	2/( square root of 300)	$\frac{2}{\sqrt{300}}$
125996	Rationalize the Denominator	17/(5+ square root of 41)	$\frac{17}{5 + \sqrt{41}}$
125997	Rationalize the Denominator	(3b^2)/(2 square root of 3ab)	$\frac{3 b^{2}}{2 \sqrt{3 a b}}$
125998	Rationalize the Denominator	3/( fourth root of 2)	$\frac{3}{\sqrt[4]{2}}$
125999	Rationalize the Denominator	3/(2+ square root of 23)	$\frac{3}{2 + \sqrt{23}}$
126000	Rationalize the Denominator	2/( cube root of x^2)	$\frac{2}{\sqrt[3]{x^{2}}}$