Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
200401	Simplify the Radical Expression	4 square root of 15( square root of 6+ square root of 5)	$4 \sqrt{15} (\sqrt{6} + \sqrt{5})$
200402	Rationalize the Denominator	(7+5i)/(-7i)	$\frac{7 + 5 i}{- 7 i}$
200403	Find the Roots (Zeros)	S(r)=r^5+4r^4-13r^3-10r^2-12r+72	$S (r) = r^{5} + 4 r^{4} - 13 r^{3} - 10 r^{2} - 12 r + 72$
200404	Evaluate	( square root of 48)/( square root of 27)	$\frac{\sqrt{48}}{\sqrt{27}}$
200405	Simplify	((-(14x)^0y^-7z)^-2)/((y^-3z)^-2)	$\frac{{(- {(14 x)}^{0} y^{- 7} z)}^{- 2}}{{(y^{- 3} z)}^{- 2}}$
200406	Solve for x	7/(x-3)-(10x)/(6x+9)=5/3	$\frac{7}{x - 3} - \frac{10 x}{6 x + 9} = \frac{5}{3}$
200407	Solve by Factoring	3x^2=-12-5x	$3 x^{2} = - 12 - 5 x$
200408	Factor	10x-2xy+35-7y	$10 x - 2 x y + 35 - 7 y$
200409	Solve for y	1-2/(3y)=6/15	$1 - \frac{2}{3 y} = \frac{6}{15}$
200410	Solve for h	-9+3h=2h+7-h	$- 9 + 3 h = 2 h + 7 - h$
200411	Simplify	(3^2x^-3y^-4)/(2^-1x^-4y^-5)	$\frac{3^{2} x^{- 3} y^{- 4}}{2^{- 1} x^{- 4} y^{- 5}}$
200412	Solve for Y	x-2Y=3	$x - 2 Y = 3$
200413	Solve the System of Equations	y-x=2 y=-1/4x+7	$y - x = 2$ $y = - \frac{1}{4} x + 7$
200414	Solve for x	7/(4x+3)=2	$\frac{7}{4 x + 3} = 2$
200415	Simplify	(mx^2-my^2)/(2m+8)*(3m+12)/(my+mx)	$\frac{m x^{2} - m y^{2}}{2 m + 8} \cdot \frac{3 m + 12}{m y + m x}$
200416	Simplify	(12x^5y^3)/(4x^-1)	$\frac{12 x^{5} y^{3}}{4 x^{- 1}}$
200417	Solve for y	5.4/(2y)=9	$\frac{5.4}{2 y} = 9$
200418	Write as a Single Logarithm	-3 natural log of x-3 natural log of y+3 natural log of z	$- 3 \ln (x) - 3 \ln (y) + 3 \ln (z)$
200419	Solve the Inequality for N	X^2-4NX+4M>0	$X^{2} - 4 N X + 4 M > 0$
200420	Solve for a	4=ga	$4 = g a$
200421	Simplify	(18w^(1/3)v^(5/4))/(27w^(4/3)v^(1/2))	$\frac{18 w^{\frac{1}{3}} v^{\frac{5}{4}}}{27 w^{\frac{4}{3}} v^{\frac{1}{2}}}$
200422	Simplify	(2x^-3y^-2)/(z^4)	$\frac{2 x^{- 3} y^{- 2}}{z^{4}}$
200423	Simplify the Radical Expression	9/( square root of 3+ square root of 7)	$\frac{9}{\sqrt{3} + \sqrt{7}}$
200424	Simplify	5x^2y^3*(-2 3/4xy^6)	$5 x^{2} y^{3} \cdot (- 2 \frac{3}{4} x y^{6})$
200425	Simplify the Radical Expression	( cube root of 24^4)/24	$\frac{\sqrt[3]{24^{4}}}{24}$
200426	Solve for x	1/2x^(5/2)=16	$\frac{1}{2} x^{\frac{5}{2}} = 16$
200427	Write in Standard Form	(2a^2b-5b^3+4a^4b^2)-(7b^3+8a^4b^2-7a^2b)	$(2 a^{2} b - 5 b^{3} + 4 a^{4} b^{2}) - (7 b^{3} + 8 a^{4} b^{2} - 7 a^{2} b)$
200428	Graph	x+3y<-18 5x+2y<=14	$x + 3 y < - 18$ $5 x + 2 y \leq 14$
200429	Simplify	(6y^2+y-2)(2y-1)^-1	$(6 y^{2} + y - 2) {(2 y - 1)}^{- 1}$
200430	Simplify	( square root of x- square root of x+1)/( square root of x+ square root of x+1)	$\frac{\sqrt{x} - \sqrt{x + 1}}{\sqrt{x} + \sqrt{x + 1}}$
200431	Solve for x	1/x+5=1/2	$\frac{1}{x} + 5 = \frac{1}{2}$
200432	Solve for x	5/x-2=5/4	$\frac{5}{x} - 2 = \frac{5}{4}$
200433	Simplify	(3a)/(b^2)*(ab+b^2)/9	$\frac{3 a}{b^{2}} \cdot \frac{a b + b^{2}}{9}$
200434	Solve for x	3x^2-7x-9=4x^2-4x-9	$3 x^{2} - 7 x - 9 = 4 x^{2} - 4 x - 9$
200435	Solve for x	-(2-3x)+x=9-x	$- (2 - 3 x) + x = 9 - x$
200436	Simplify the Radical Expression	cube root of 3/(4k)	$\sqrt[3]{\frac{3}{4 k}}$
200437	Solve for x	4/(3(x+2))-2/(3x)=1/(x+2)	$\frac{4}{3 (x + 2)} - \frac{2}{3 x} = \frac{1}{x + 2}$
200438	Simplify	6 square root of 3ab*4 square root of 24ab^3	$6 \sqrt{3 a b} \cdot 4 \sqrt{24 a b^{3}}$
200439	Find the Complex Conjugate	square root of 6-3	$\sqrt{6} - 3$
200440	Write in Slope-Intercept Form	y+17=3(x+6)-14	$y + 17 = 3 (x + 6) - 14$
200441	Solve the System of Inequalities	3x+12>=-9 and 9x-3<=33	$3 x + 12 \geq - 9$ and $9 x - 3 \leq 33$
200442	Simplify	((x^2-3x-10)/(x+3))/((2x^2-7x-15)/(x^2-9))	$\frac{\frac{x^{2} - 3 x - 10}{x + 3}}{\frac{2 x^{2} - 7 x - 15}{x^{2} - 9}}$
200443	Simplify	(5a+b^2)/(8b)-(5a-7b^2)/(8b)	$\frac{5 a + b^{2}}{8 b} - \frac{5 a - 7 b^{2}}{8 b}$
200444	Simplify the Radical Expression	cube root of 750+ cube root of 2058- cube root of 48	$\sqrt[3]{750} + \sqrt[3]{2058} - \sqrt[3]{48}$
200445	Solve for z	square root of (z+1)^2=2	$\sqrt{{(z + 1)}^{2}} = 2$
200446	Simplify	( square root of 18x+4 square root of 8x- square root of 50x)	$(\sqrt{18 x} + 4 \sqrt{8 x} - \sqrt{50 x})$
200447	Evaluate	(6 5/6-5 3/8)÷(7/48)	$(6 \frac{5}{6} - 5 \frac{3}{8}) \div \frac{7}{48}$
200448	Solve for x	9/(15x)+1/5=2/5	$\frac{9}{15 x} + \frac{1}{5} = \frac{2}{5}$
200449	Solve for x	2/x=4/(2x)-2	$\frac{2}{x} = \frac{4}{2 x} - 2$
200450	Solve for f	fg=5	$f g = 5$
200451	Find the Product	(x^2+10x+100)(x-10)	$(x^{2} + 10 x + 100) (x - 10)$
200452	Solve the Inequality for t	7+t<=2(t+3)+2	$7 + t \leq 2 (t + 3) + 2$
200453	Find the Directrix	(x-1)^2+8(y+2)=0	${(x - 1)}^{2} + 8 (y + 2) = 0$
200454	Solve for x	square root of 4-x- square root of 3-x=1	$\sqrt{4 - x} - \sqrt{3 - x} = 1$
200455	Simplify the Radical Expression	( square root of 3)/( square root of 8)	$\frac{\sqrt{3}}{\sqrt{8}}$
200456	Simplify the Radical Expression	( cube root of 6* cube root of 72)/( cube root of 2)	$\frac{\sqrt[3]{6} \cdot \sqrt[3]{72}}{\sqrt[3]{2}}$
200457	Simplify	(6y^2+8y^4-5y)-(9y^4-7y+2y^2)	$(6 y^{2} + 8 y^{4} - 5 y) - (9 y^{4} - 7 y + 2 y^{2})$
200458	Simplify	4 square root of 2x*3 square root of 8x	$4 \sqrt{2 x} \cdot 3 \sqrt{8 x}$
200459	Simplify	16/( fourth root of 16^3)	$\frac{16}{\sqrt[4]{16^{3}}}$
200460	Simplify	(35x^5y)÷((7x^3)/34)	$35 x^{5} y \div \frac{7 x^{3}}{34}$
200461	Simplify	((2^6)/(5^3))^(-1/3)	${(\frac{2^{6}}{5^{3}})}^{- \frac{1}{3}}$
200462	Evaluate	2 3/4÷(1 1/2-2/5)	$2 \frac{3}{4} \div (1 \frac{1}{2} - \frac{2}{5})$
200463	Solve the Inequality for t	t-3>-8	$t - 3 > - 8$
200464	Simplify	3/4(24x+28)-(4x-1)	$\frac{3}{4} (24 x + 28) - (4 x - 1)$
200465	Solve for y	square root of 25y^2+40y+16=5y+4	$\sqrt{25 y^{2} + 40 y + 16} = 5 y + 4$
200466	Simplify	((-9p^(1/2)q)^0)^-1	${({(- 9 p^{\frac{1}{2}} q)}^{0})}^{- 1}$
200467	Solve the System of Equations	2x-6y=30 y=1/3x+1	$2 x - 6 y = 30$ $y = \frac{1}{3} x + 1$
200468	Solve for x	2 square root of x-8<24	$2 \sqrt{x - 8} < 24$
200469	Solve for h	-6+6h=9h	$- 6 + 6 h = 9 h$
200470	Simplify	((30x+15)/x)÷(10/(3x))	$\frac{30 x + 15}{x} \div \frac{10}{3 x}$
200471	Factor	x^5+5x^2-4x^3-20	$x^{5} + 5 x^{2} - 4 x^{3} - 20$
200472	Find the Domain and Range	f(x)=1/2 cube root of x+6	$f (x) = \frac{1}{2} \sqrt[3]{x + 6}$
200473	Expand the Logarithmic Expression	natural log of (3r^2)/(r-8)	$\ln (\frac{3 r^{2}}{r - 8})$
200474	Solve for x	2/x+3/x=1/(x-4)	$\frac{2}{x} + \frac{3}{x} = \frac{1}{x - 4}$
200475	Solve for x	7=(2x+46)/8	$7 = \frac{2 x + 46}{8}$
200476	Simplify	(-3)^(1/3)(-3)^(1/3)(-3)^(1/3)	${(- 3)}^{\frac{1}{3}} \cdot {(- 3)}^{\frac{1}{3}} \cdot {(- 3)}^{\frac{1}{3}}$
200477	Solve for w	-1/3=-5/6+w	$- \frac{1}{3} = - \frac{5}{6} + w$
200478	Solve the System of Inequalities	11x+4<15 or 12x-7>-25	$11 x + 4 < 15$ or $12 x - 7 > - 25$
200479	Solve for j	-9-7j+4=2-6j	$- 9 - 7 j + 4 = 2 - 6 j$
200480	Solve for c	10^2+10^2=c^2	$10^{2} + 10^{2} = c^{2}$
200481	Solve for x	x-5(x-1)=x-(2x-3)	$x - 5 (x - 1) = x - (2 x - 3)$
200482	Simplify the Radical Expression	fourth root of 5x* fourth root of 2x	$\sqrt[4]{5 x} \cdot \sqrt[4]{2 x}$
200483	Simplify	(a^-5b^8c^-12)(a^7b^-3c^7)	$(a^{- 5} b^{8} c^{- 12}) (a^{7} b^{- 3} c^{7})$
200484	Simplify	(2m^2)^-1(4m^(3/2))	${(2 m^{2})}^{- 1} (4 m^{\frac{3}{2}})$
200485	Solve the Rational Equation for m	fourth root of 2m=4	$\sqrt[4]{2 m} = 4$
200486	Expand the Logarithmic Expression	log base 6 of square root of 3mn^8	$\log_{6} (\sqrt{3 m n^{8}})$
200487	Evaluate	(-(w^3)/6)^-2	${(- \frac{w^{3}}{6})}^{- 2}$
200488	Simplify	( fifth root of -8)^8	${(\sqrt[5]{- 8})}^{8}$
200489	Rationalize the Denominator	2/( cube root of 4-3)	$\frac{2}{\sqrt[3]{4} - 3}$
200490	Solve for x	log base (x+3) of 125=3	$\log_{(x + 3)} (125) = 3$
200491	Solve for c	(2c-1)/9+c/4=(c+3)/6	$\frac{2 c - 1}{9} + \frac{c}{4} = \frac{c + 3}{6}$
200492	Solve for x	6/(x+16)=7/(3x+3)	$\frac{6}{x + 16} = \frac{7}{3 x + 3}$
200493	Find the Roots (Zeros)	f(x)=tan(3x)	$f (x) = \tan (3 x)$
200494	Solve for d	1.8(6.4d+4)=1.6(8.3d+6.7)	$1.8 (6.4 d + 4) = 1.6 (8.3 d + 6.7)$
200495	Solve for k	-7(k+5)=3k-(8k-1)	$- 7 (k + 5) = 3 k - (8 k - 1)$
200496	Simplify the Radical Expression	(3 cube root of 2)/( cube root of 3)	$\frac{3 \sqrt[3]{2}}{\sqrt[3]{3}}$
200497	Solve for x	7/(10x)=3/20+2	$\frac{7}{10 x} = \frac{3}{20} + 2$
200498	Solve for x	(6x)/7-3=2x	$\frac{6 x}{7} - 3 = 2 x$
200499	Simplify	-(-5a^-2bc)^0	$- {(- 5 a^{- 2} b c)}^{0}$
200500	Solve for z	(3z)/2+1/4=7/8	$\frac{3 z}{2} + \frac{1}{4} = \frac{7}{8}$