Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
6801	Convert to Interval Notation	(x-4)(x+3)(1-x)>0	$(x - 4) (x + 3) (1 - x) > 0$
6802	Convert to Interval Notation	(x-3)(x+5)>0	$(x - 3) (x + 5) > 0$
6803	Convert to Interval Notation	(x-4)(x+5)(2-x)>0	$(x - 4) (x + 5) (2 - x) > 0$
6804	Convert to Interval Notation	(x+6)(x-3)(x-7)<0	$(x + 6) (x - 3) (x - 7) < 0$
6805	Convert to Interval Notation	(x-2)(x+9)>0	$(x - 2) (x + 9) > 0$
6806	Simplify	1- square root of 3	$1 - \sqrt{3}$
6807	Simplify	3^2+3^2+ square root of 18	$3^{2} + 3^{2} + \sqrt{18}$
6808	Simplify	3 square root of 200+2 square root of 8	$3 \sqrt{200} + 2 \sqrt{8}$
6809	Simplify	3- square root of 12	$3 - \sqrt{12}$
6810	Simplify	3 square root of 54-2 square root of 24- square root of 96+4 square root of 63	$3 \sqrt{54} - 2 \sqrt{24} - \sqrt{96} + 4 \sqrt{63}$
6811	Simplify	72-7 square root of 7	$72 - 7 \sqrt{7}$
6812	Write with Rational (Fractional) Exponents	cos(arctan( square root of 13))	$\cos (\arctan (\sqrt{13}))$
6813	Write with Rational (Fractional) Exponents	sin(arccos(( square root of 26)/26))	$\sin (\arccos (\frac{\sqrt{26}}{26}))$
6814	Write with Rational (Fractional) Exponents	tan(arcsec(-2/( square root of 3)))	$\tan (arcsec (- \frac{2}{\sqrt{3}}))$
6815	Write with Rational (Fractional) Exponents	tan( square root of 3)	$\tan (\sqrt{3})$
6816	Simplify	( square root of 2)/2-1/2	$\frac{\sqrt{2}}{2} - \frac{1}{2}$
6817	Simplify	1/9*(13-2 square root of 22)	$\frac{1}{9} \cdot (13 - 2 \sqrt{22})$
6818	Write with Rational (Fractional) Exponents	arctan(-1/( square root of 3))	$\arctan (\frac{- 1}{\sqrt{3}})$
6819	Write with Rational (Fractional) Exponents	arctan(-( square root of 3)/3)	$\arctan (- \frac{\sqrt{3}}{3})$
6820	Write with Rational (Fractional) Exponents	5 fifth root of 5ab	$5 \sqrt[5]{5 a b}$
6821	Write with Rational (Fractional) Exponents	fourth root of 96x^12w^5	$\sqrt[4]{96 x^{12} w^{5}}$
6822	Write with Rational (Fractional) Exponents	fifth root of 243^3	$\sqrt[5]{243^{3}}$
6823	Write with Rational (Fractional) Exponents	cube root of 8x^7	$\sqrt[3]{8 x^{7}}$
6824	Write with Rational (Fractional) Exponents	sixth root of x^12y^15	$\sqrt[6]{x^{12} y^{15}}$
6825	Write with Rational (Fractional) Exponents	3a square root of 30a^3c^5	$3 a \sqrt{30 a^{3} c^{5}}$
6826	Write with Rational (Fractional) Exponents	square root of sec(x)^2-1	$\sqrt{\sec^{2} (x) - 1}$
6827	Write with Rational (Fractional) Exponents	1/( square root of 2)	$\frac{1}{\sqrt{2}}$
6828	Write with Rational (Fractional) Exponents	square root of 527	$\sqrt{527}$
6829	Write with Rational (Fractional) Exponents	square root of 2-2cos(x)	$\sqrt{2 - 2 \cos (x)}$
6830	Write with Rational (Fractional) Exponents	- square root of 128	$- \sqrt{128}$
6831	Write with Rational (Fractional) Exponents	square root of 91	$\sqrt{91}$
6832	Write with Rational (Fractional) Exponents	square root of 77	$\sqrt{77}$
6833	Write with Rational (Fractional) Exponents	cube root of a^2b^3 cube root of a^10b	$\sqrt[3]{a^{2} b^{3}} \sqrt[3]{a^{10} b}$
6834	Write with Rational (Fractional) Exponents	square root of x-5	$\sqrt{x - 5}$
6835	Find the Roots/Zeros Using the Rational Roots Test	x^5+3x^4-9x^3-31x^2+36	$x^{5} + 3 x^{4} - 9 x^{3} - 31 x^{2} + 36$
6836	Find the Roots/Zeros Using the Rational Roots Test	x^6-64	$x^{6} - 64$
6837	Find the Roots/Zeros Using the Rational Roots Test	x^6+16x^3+64	$x^{6} + 16 x^{3} + 64$
6838	Find the Roots/Zeros Using the Rational Roots Test	2x^3+12x^2+10x	$2 x^{3} + 12 x^{2} + 10 x$
6839	Find the Roots/Zeros Using the Rational Roots Test	10x^3-17^2-7+2	$10 x^{3} - 17^{2} - 7 + 2$
6840	Find the Roots/Zeros Using the Rational Roots Test	2x^3+3x^2-8x+3	$2 x^{3} + 3 x^{2} - 8 x + 3$
6841	Find the Roots/Zeros Using the Rational Roots Test	2x^4+x^3+7x^2+4x-4	$2 x^{4} + x^{3} + 7 x^{2} + 4 x - 4$
6842	Find the Roots/Zeros Using the Rational Roots Test	2x^4-x^3-19x^2+9x+9	$2 x^{4} - x^{3} - 19 x^{2} + 9 x + 9$
6843	Find the Roots/Zeros Using the Rational Roots Test	2x^4-x^3-26x^2-11x+12	$2 x^{4} - x^{3} - 26 x^{2} - 11 x + 12$
6844	Find the Roots/Zeros Using the Rational Roots Test	2x^4+x^3-17x^2-4x+6	$2 x^{4} + x^{3} - 17 x^{2} - 4 x + 6$
6845	Find the Roots/Zeros Using the Rational Roots Test	4x^5-8x^4-5x^3+10x^2+x-2	$4 x^{5} - 8 x^{4} - 5 x^{3} + 10 x^{2} + x - 2$
6846	Find the Roots/Zeros Using the Rational Roots Test	4x^4+17x^3-11x^2+17x-15	$4 x^{4} + 17 x^{3} - 11 x^{2} + 17 x - 15$
6847	Find the Roots/Zeros Using the Rational Roots Test	3x^4-22x^3+64x^2-58x+13	$3 x^{4} - 22 x^{3} + 64 x^{2} - 58 x + 13$
6848	Find the Roots/Zeros Using the Rational Roots Test	4x^4-22x^3+36x^2-44x+56	$4 x^{4} - 22 x^{3} + 36 x^{2} - 44 x + 56$
6849	Find the Roots/Zeros Using the Rational Roots Test	4x^4-22x^3+38x^2-44x+60	$4 x^{4} - 22 x^{3} + 38 x^{2} - 44 x + 60$
6850	Find the Roots/Zeros Using the Rational Roots Test	3x-6	$3 x - 6$
6851	Find the Roots/Zeros Using the Rational Roots Test	-4x^2+4x-1	$- 4 x^{2} + 4 x - 1$
6852	Find the Roots/Zeros Using the Rational Roots Test	4x^3-33x^2+72x-16	$4 x^{3} - 33 x^{2} + 72 x - 16$
6853	Find the Roots/Zeros Using the Rational Roots Test	-3x^3+20x^2-36x+16	$- 3 x^{3} + 20 x^{2} - 36 x + 16$
6854	Find the Roots/Zeros Using the Rational Roots Test	3x^3-4x^2-12x+16	$3 x^{3} - 4 x^{2} - 12 x + 16$
6855	Find the Roots/Zeros Using the Rational Roots Test	3x^4-11x^3-x^2+19x+6	$3 x^{4} - 11 x^{3} - x^{2} + 19 x + 6$
6856	Find the Roots/Zeros Using the Rational Roots Test	3x^4-7x^3-37x^2-17x+10	$3 x^{4} - 7 x^{3} - 37 x^{2} - 17 x + 10$
6857	Find the Roots/Zeros Using the Rational Roots Test	2x+10+2x+10+3	$2 x + 10 + 2 x + 10 + 3$
6858	Find the Roots/Zeros Using the Rational Roots Test	2x^5-8x^4-60x^3+48x^2+106y-88	$2 x^{5} - 8 x^{4} - 60 x^{3} + 48 x^{2} + 106 y - 88$
6859	Find the Roots/Zeros Using the Rational Roots Test	25t^3-65t^2+71t+17	$25 t^{3} - 65 t^{2} + 71 t + 17$
6860	Find the Roots/Zeros Using the Rational Roots Test	9x^5-27x^4-10x^3+30x^2+x-3	$9 x^{5} - 27 x^{4} - 10 x^{3} + 30 x^{2} + x - 3$
6861	Find the Roots/Zeros Using the Rational Roots Test	5x^3-33x^2+58x-24	$5 x^{3} - 33 x^{2} + 58 x - 24$
6862	Find the Roots/Zeros Using the Rational Roots Test	6x^4-11x^3-51x^2+99x-27	$6 x^{4} - 11 x^{3} - 51 x^{2} + 99 x - 27$
6863	Find the Roots/Zeros Using the Rational Roots Test	5x^3-9x^2-12x-2	$5 x^{3} - 9 x^{2} - 12 x - 2$
6864	Find the Roots/Zeros Using the Rational Roots Test	6x^2-7x-20	$6 x^{2} - 7 x - 20$
6865	Find the Roots/Zeros Using the Rational Roots Test	8x^4-14x^3-71x^2-10x+24	$8 x^{4} - 14 x^{3} - 71 x^{2} - 10 x + 24$
6866	Find the Roots/Zeros Using the Rational Roots Test	5x^3-7x^2-45x+63	$5 x^{3} - 7 x^{2} - 45 x + 63$
6867	Find the Roots/Zeros Using the Rational Roots Test	9x^4-9x^3-58x^2+4x+24	$9 x^{4} - 9 x^{3} - 58 x^{2} + 4 x + 24$
6868	Convert to Radical Form	(a^(3/4))^5	${(a^{\frac{3}{4}})}^{5}$
6869	Convert to Radical Form	(9-y)^(1/3)	${(9 - y)}^{\frac{1}{3}}$
6870	Convert to Radical Form	(125x^6y^7)^(1/3)	${(125 x^{6} y^{7})}^{\frac{1}{3}}$
6871	Convert to Radical Form	(2x)^(7/6)	${(2 x)}^{\frac{7}{6}}$
6872	Convert to Radical Form	(2x^6-x^(1/2)-x)*(x^(1/2)-3x)	$(2 x^{6} - x^{\frac{1}{2}} - x) \cdot (x^{\frac{1}{2}} - 3 x)$
6873	Convert to Radical Form	e^(1/2)	$e^{\frac{1}{2}}$
6874	Convert to Radical Form	a^(15/4)*a^(-7/4)	$a^{\frac{15}{4}} \cdot a^{- \frac{7}{4}}$
6875	Convert to Radical Form	z^(1/2)	$z^{\frac{1}{2}}$
6876	Convert to Radical Form	3x^(2/5)-4x^(1/3)	$3 x^{\frac{2}{5}} - 4 x^{\frac{1}{3}}$
6877	Convert to Radical Form	6x^(1/4)y^(1/2)	$6 x^{\frac{1}{4}} y^{\frac{1}{2}}$
6878	Convert to Radical Form	9x^(4/3)	$9 x^{\frac{4}{3}}$
6879	Write with Rational (Fractional) Exponents	(11 root of 11)^12	${(\sqrt[11]{11})}^{12}$
6880	Convert to Radical Form	9^(1/2)	$9^{\frac{1}{2}}$
6881	Convert to Radical Form	e^(-3/4)	$e^{- \frac{3}{4}}$
6882	Convert to Radical Form	(2tan(22.5))/(1-tan(22.5)^2)	$\frac{2 \tan (22.5)}{1 - \tan^{2} (22.5)}$
6883	Convert to Radical Form	2^(8/7)	$2^{\frac{8}{7}}$
6884	Convert to Radical Form	(27^(-2/3))/(27^(-1/3))	$\frac{27^{- \frac{2}{3}}}{27^{- \frac{1}{3}}}$
6885	Convert to Radical Form	(a+b)^(7/10)	${(a + b)}^{\frac{7}{10}}$
6886	Write with Rational (Fractional) Exponents	( square root of 245x^3)/(y^5)	$\frac{\sqrt{245 x^{3}}}{y^{5}}$
6887	Write with Rational (Fractional) Exponents	( square root of 80)/64	$\frac{\sqrt{80}}{64}$
6888	Write with Rational (Fractional) Exponents	(3 square root of x-6 square root of y)(3 square root of x+6 square root of y)	$(3 \sqrt{x} - 6 \sqrt{y}) (3 \sqrt{x} + 6 \sqrt{y})$
6889	Write with Rational (Fractional) Exponents	(ab cube root of 2a^2b^2)(2a cube root of 4ab^2)	$(a b \sqrt[3]{2 a^{2} b^{2}}) (2 a \sqrt[3]{4 a b^{2}})$
6890	Write with Rational (Fractional) Exponents	(1/3+( square root of 13)/6*i)^2	${(\frac{1}{3} + \frac{\sqrt{13}}{6} \cdot i)}^{2}$
6891	Write with Rational (Fractional) Exponents	(1/( square root of x+h)-1/( square root of x))/h	$\frac{\frac{1}{\sqrt{x + h}} - \frac{1}{\sqrt{x}}}{h}$
6892	Convert to Radical Form	4x^(1/2)y^(3/4)-8x^(3/2)y^(1/4)	$4 x^{\frac{1}{2}} y^{\frac{3}{4}} - 8 x^{\frac{3}{2}} y^{\frac{1}{4}}$
6893	Evaluate	log base 5 of 63.2	$\log_{5} (63.2)$
6894	Write with Rational (Fractional) Exponents	square root of (3.9-(-0.1))^2+(2.5-0.8)^2	$\sqrt{{(3.9 - (- 0.1))}^{2} + {(2.5 - 0.8)}^{2}}$
6895	Write with Rational (Fractional) Exponents	seventh root of m square root of m	$\sqrt[7]{m} \sqrt{m}$
6896	Write with Rational (Fractional) Exponents	(1/( square root of x-h)-1/( square root of x))/h	$\frac{\frac{1}{\sqrt{x - h}} - \frac{1}{\sqrt{x}}}{h}$
6897	Write with Rational (Fractional) Exponents	( square root of b-v)( square root of b+v)	$(\sqrt{b} - v) (\sqrt{b + v})$
6898	Solve Using the Quadratic Formula	x^2+12x-300=0	$x^{2} + 12 x - 300 = 0$
6899	Solve Using the Quadratic Formula	x^2+14x+42=-5	$x^{2} + 14 x + 42 = - 5$
6900	Solve Using the Quadratic Formula	x^2+2x=46	$x^{2} + 2 x = 46$