Mathway | Popular Problems

Popular Problems

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Rank	Topic	Problem	Formatted Problem
68001	Simplify	(9-4 square root of 3y)(3+6 square root of 21x)	$(9 - 4 \sqrt{3 y}) (3 + 6 \sqrt{21 x})$
68002	Simplify	(1/2+( square root of 3)/2*i)^2	${(\frac{1}{2} + \frac{\sqrt{3}}{2} \cdot i)}^{2}$
68003	Multiply	12*7	$12 \cdot 7$
68004	Multiply	square root of -5* square root of -10	$\sqrt{- 5} \cdot \sqrt{- 10}$
68005	Evaluate Using the Given Value	f(1)=7	$f (1) = 7$
68006	Multiply	-12x(6x-11)	$- 12 x (6 x - 11)$
68007	Multiply	-3a^2(5a^2-3a+5)	$- 3 a^{2} (5 a^{2} - 3 a + 5)$
68008	Multiply	6x(7x+5)	$6 x (7 x + 5)$
68009	Evaluate Using the Given Value	y=20 , 0(1.03^25)	$y = 20$ , $0 ({1.03}^{25})$
68010	Simplify	(x/4-1/x)/(1-2/x)	$\frac{\frac{x}{4} - \frac{1}{x}}{1 - \frac{2}{x}}$
68011	Simplify	( fourth root of 27)/( fourth root of 6)	$\frac{\sqrt[4]{27}}{\sqrt[4]{6}}$
68012	Evaluate Using the Given Value	f(6)=(6-7)^2	$f (6) = {(6 - 7)}^{2}$
68013	Simplify	( fourth root of y^2)/( sixth root of y^2)	$\frac{\sqrt[4]{y^{2}}}{\sqrt[6]{y^{2}}}$
68014	Evaluate Using the Given Value	f(9)=(9-7)^2	$f (9) = {(9 - 7)}^{2}$
68015	Simplify	( cube root of 9x^2)/( cube root of 3x)	$\frac{\sqrt[3]{9 x^{2}}}{\sqrt[3]{3 x}}$
68016	Simplify	(x^2+2x-15)/(x^2+6x+5)	$\frac{x^{2} + 2 x - 15}{x^{2} + 6 x + 5}$
68017	Evaluate Using the Given Value	f(6) = square root of 6+3	$f (6) = \sqrt{6 + 3}$
68018	Evaluate Using the Given Value	f(-3)=3	$f (- 3) = 3$
68019	Simplify	(x^(1/3))/(x^(-3/4)x^(1/4))	$\frac{x^{\frac{1}{3}}}{x^{- \frac{3}{4}} x^{\frac{1}{4}}}$
68020	Evaluate Using the Given Value	f(11) = cube root of 11-3	$f (11) = \sqrt[3]{11 - 3}$
68021	Simplify	(x^2-64)/(x^2+16x+64)	$\frac{x^{2} - 64}{x^{2} + 16 x + 64}$
68022	Simplify	(x^2-81)/(9-x)	$\frac{x^{2} - 81}{9 - x}$
68023	Simplify	(x^2-10x-24)/(x^2-3x-108)	$\frac{x^{2} - 10 x - 24}{x^{2} - 3 x - 108}$
68024	Simplify	(x^2-49)/(x^2+14x+49)	$\frac{x^{2} - 49}{x^{2} + 14 x + 49}$
68025	Simplify	(x^2-4x+4)/(x^2-4)	$\frac{x^{2} - 4 x + 4}{x^{2} - 4}$
68026	Evaluate Using the Given Value	f(2)=3(2)^2-(2)-2	$f (2) = 3 {(2)}^{2} - (2) - 2$
68027	Simplify	(v((2x)^2))/(v((5y)^4))	$\frac{v ({(2 x)}^{2})}{v ({(5 y)}^{4})}$
68028	Simplify	( square root of 32a^7b^2)/( square root of 2a^3b)	$\frac{\sqrt{32 a^{7} b^{2}}}{\sqrt{2 a^{3} b}}$
68029	Evaluate Using the Given Value	f(4)=0.016(4)^2+0.124(4)+0.787	$f (4) = 0.016 {(4)}^{2} + 0.124 (4) + 0.787$
68030	Simplify	square root of 14y^14z	$\sqrt{14 y^{14} z}$
68031	Simplify	( square root of -4)/((5+2i)-(3-4i))	$\frac{\sqrt{- 4}}{(5 + 2 i) - (3 - 4 i)}$
68032	Simplify	( square root of 2)/( square root of 14x)	$\frac{\sqrt{2}}{\sqrt{14 x}}$
68033	Simplify	( square root of 20x^3)/( square root of 5x)	$\frac{\sqrt{20 x^{3}}}{\sqrt{5 x}}$
68034	Evaluate Using the Given Value	f(5)=2(5)^2-5	$f (5) = 2 {(5)}^{2} - 5$
68035	Simplify	( square root of -56)/( square root of -7)	$\frac{\sqrt{- 56}}{\sqrt{- 7}}$
68036	Evaluate Using the Given Value	f(54)=545(1.026)^54	$f (54) = 545 {(1.026)}^{54}$
68037	Simplify	( square root of 7)/( square root of 11)	$\frac{\sqrt{7}}{\sqrt{11}}$
68038	Simplify	( square root of 6)/( square root of 3y)	$\frac{\sqrt{6}}{\sqrt{3 y}}$
68039	Evaluate Using the Given Value	f(4)=2(4)+3	$f (4) = 2 (4) + 3$
68040	Evaluate Using the Given Value	log base 1/2 of 462	$\log_{\frac{1}{2}} (462)$
68041	Simplify	( square root of 9x)/2	$\frac{\sqrt{9 x}}{2}$
68042	Simplify	( square root of 75x^3)/( square root of 3x)	$\frac{\sqrt{75 x^{3}}}{\sqrt{3 x}}$
68043	Simplify	( square root of y)/( square root of 5)	$\frac{\sqrt{y}}{\sqrt{5}}$
68044	Simplify	( cube root of x-9)^3	${(\sqrt[3]{x - 9})}^{3}$
68045	Simplify	( cube root of 24x^5y^2)/( cube root of 3x^2y)	$\frac{\sqrt[3]{24 x^{5} y^{2}}}{\sqrt[3]{3 x^{2} y}}$
68046	Simplify	(4/x+7)/(16/(x^2)-49)	$\frac{\frac{4}{x} + 7}{\frac{16}{x^{2}} - 49}$
68047	Evaluate Using the Given Value	f(0)=6	$f (0) = 6$
68048	Evaluate Using the Given Value	x=-1 plus or minus i	$x = - 1 \pm i$
68049	Simplify	(4/x+1/(x^2))/(16/(x^2)-1/x)	$\frac{\frac{4}{x} + \frac{1}{x^{2}}}{\frac{16}{x^{2}} - \frac{1}{x}}$
68050	Evaluate Using the Given Value	f(12) = square root of 5(12)+4	$f (12) = \sqrt{5 (12) + 4}$
68051	Simplify	((4x^2+12x-16)/(2x+10))/((6x+24)/(x^2+9x+20))	$\frac{\frac{4 x^{2} + 12 x - 16}{2 x + 10}}{\frac{6 x + 24}{x^{2} + 9 x + 20}}$
68052	Evaluate Using the Given Value	f(-5) = square root of -5+3	$f (- 5) = \sqrt{- 5 + 3}$
68053	Evaluate Using the Given Value	f(-6)=4(-6)+4	$f (- 6) = 4 (- 6) + 4$
68054	Simplify	(1/x+1)/(1/x-1)	$\frac{\frac{1}{x} + 1}{\frac{1}{x} - 1}$
68055	Simplify	(p^2-3p-10)/(p^2+p-2)	$\frac{p^{2} - 3 p - 10}{p^{2} + p - 2}$
68056	Simplify	(5/x+7)/(25/(x^2)-49)	$\frac{\frac{5}{x} + 7}{\frac{25}{x^{2}} - 49}$
68057	Simplify	(7 square root of x)^2	${(7 \sqrt{x})}^{2}$
68058	Simplify	((2hj^2k^-2*(h^4j^-1k^4))^0)/(2h^-3j^-4k^-2)	$\frac{{(2 h j^{2} k^{- 2} \cdot (h^{4} j^{- 1} k^{4}))}^{0}}{2 h^{- 3} j^{- 4} k^{- 2}}$
68059	Simplify	(((x+4)^2)/(x-4))/((x^2-16)/(4x-16))	$\frac{\frac{{(x + 4)}^{2}}{x - 4}}{\frac{x^{2} - 16}{4 x - 16}}$
68060	Simplify	(3i)/(4+2i)	$\frac{3 i}{4 + 2 i}$
68061	Simplify	(3x-6)/(x^2-4x+4)	$\frac{3 x - 6}{x^{2} - 4 x + 4}$
68062	Simplify	(3x-6)/(x-2)	$\frac{3 x - 6}{x - 2}$
68063	Evaluate Using the Given Value	f(27)=545(1.026)^27	$f (27) = 545 {(1.026)}^{27}$
68064	Simplify	(35x-35)/(25x-40)	$\frac{35 x - 35}{25 x - 40}$
68065	Simplify	fourth root of b^3 square root of b	$\sqrt[4]{b^{3}} \sqrt{b}$
68066	Simplify	4/( square root of 24x)	$\frac{4}{\sqrt{24 x}}$
68067	Evaluate Using the Given Value	f(-10) = square root of -10^2+1	$f (- 10) = \sqrt{- 10^{2} + 1}$
68068	Simplify	4/( square root of 27x)	$\frac{4}{\sqrt{27 x}}$
68069	Simplify	4/( square root of 11)	$\frac{4}{\sqrt{11}}$
68070	Simplify	(4z^2-16z+15)/(2z^2+z-15)	$\frac{4 z^{2} - 16 z + 15}{2 z^{2} + z - 15}$
68071	Evaluate Using the Given Value	f(-4)=-4^2-3	$f (- 4) = - 4^{2} - 3$
68072	Simplify	5/( square root of 11)	$\frac{5}{\sqrt{11}}$
68073	Evaluate Using the Given Value	f(8) = square root of 3(8)+1	$f (8) = \sqrt{3 (8) + 1}$
68074	Evaluate Using the Given Value	4x-10y-104x+5y=35	$4 x - 10 y - 104 x + 5 y = 35$
68075	Simplify	5/(2-i)	$\frac{5}{2 - i}$
68076	Simplify	(9x^2-25)/(3x-5)	$\frac{9 x^{2} - 25}{3 x - 5}$
68077	Evaluate Using the Given Value	f(0)=1^0	$f (0) = 1^{0}$
68078	Simplify	8/( square root of 2)	$\frac{8}{\sqrt{2}}$
68079	Simplify	8/( square root of 5x)	$\frac{8}{\sqrt{5 x}}$
68080	Evaluate Using the Given Value	f(2)=2(2)+2	$f (2) = 2 (2) + 2$
68081	Simplify	6/(3- square root of 11)	$\frac{6}{3 - \sqrt{11}}$
68082	Simplify	6/( square root of 2x)	$\frac{6}{\sqrt{2 x}}$
68083	Simplify	(6-x)/(x-6)	$\frac{6 - x}{x - 6}$
68084	Evaluate Using the Given Value	f(5)=2(5)	$f (5) = 2 (5)$
68085	Simplify	(7a)/( fifth root of 8a^7b^13)	$\frac{7 a}{\sqrt[5]{8 a^{7} b^{13}}}$
68086	Evaluate Using the Given Value	f(-6)=1/2(-6)+3	$f (- 6) = \frac{1}{2} (- 6) + 3$
68087	Simplify	(7x-28)/(x^2-16)	$\frac{7 x - 28}{x^{2} - 16}$
68088	Evaluate Using the Given Value	f(8)=(8-7)^2	$f (8) = {(8 - 7)}^{2}$
68089	Simplify	7/(2-2 square root of 3)	$\frac{7}{2 - 2 \sqrt{3}}$
68090	Evaluate Using the Given Value	x = natural log of 15 , 0	$x = \ln (15)$ , $0$
68091	Simplify	(1-2/(3x))/(x-4/(9x))	$\frac{1 - \frac{2}{3 x}}{x - \frac{4}{9 x}}$
68092	Evaluate Using the Given Value	f(13)=62+35 log of 13-4	$f (13) = 62 + 35 \log (13 - 4)$
68093	Simplify	1/( cube root of 2)	$\frac{1}{\sqrt[3]{2}}$
68094	Evaluate Using the Given Value	f(3)=5(3)^2+3(3)	$f (3) = 5 {(3)}^{2} + 3 (3)$
68095	Simplify	3/( cube root of 2)	$\frac{3}{\sqrt[3]{2}}$
68096	Simplify	-3/( square root of x-4)	$\frac{- 3}{\sqrt{x} - 4}$
68097	Simplify	square root of -98x	$\sqrt{- 98 x}$
68098	Simplify	(2r-4)/(r-2)	$\frac{2 r - 4}{r - 2}$
68099	Evaluate Using the Given Value	f(0)=0^4-36(0)^2	$f (0) = 0^{4} - 36 {(0)}^{2}$
68100	Simplify	(2x-10)/(x^2-2x-15)	$\frac{2 x - 10}{x^{2} - 2 x - 15}$