List all of the numbers in the set

1. natural numbers.

2. whole numbers.

3. integers.

4. rational numbers.

5. irrational numbers.

6. real numbers.

$3x+1=1+3x$

$\pi (x+y)=\pi x+\pi y$

$(x^2+1)\cdot 0=0\cdot (x^2+1)$

$(x^2+1)\cdot 1=x^2+1$

$[-2,3)$

$(-\infty ,1]$

$1\le x<4$

$x>0$

${\displaystyle \frac{-12}{|2|}}$

$|2-|-3||$

$|-5-|-7||$

$|1-\sqrt{15}|$

$-5^0$

${(-4)}^3$

${\displaystyle \frac{2^{18}}{2^{17}}}$

$2^4-5\cdot 3^2$

${(2^3)}^2$

$-{25}^{1/2}$

${\left({\displaystyle \frac{1}{16}}\right)}^{1/4}$

$8^{4/3}$

${(-27)}^{2/3}$

${\left({\displaystyle \frac{25}{36}}\right)}^{-3/2}$

${81}^{-3/2}$

$2\cdot 5^3$

$3^2\cdot 2^5$

${\displaystyle \frac{21\times {10}^6}{3\times {10}^7}}$

$\sqrt[4]{10,000}$

$\sqrt{5^2}$

$\sqrt{{(-9)}^2}$

$\sqrt[3]{-125}$

$3^{1/2}\cdot {27}^{1/2}$

${64}^{-1/3}$

$\sqrt{5}\sqrt{20}$

$(\sqrt{3}+2)(\sqrt{3}-2)$

${\left({\displaystyle \frac{1}{16}}\right)}^{-3/2}$

${\displaystyle \frac{3^{-2}\cdot 7^0}{{18}^{-1}}}$

$4(x+7)+2y;x=3,y=4$

${\displaystyle \frac{y-6\sqrt{x}}{xy}};x=4,y=2$

${\displaystyle \frac{|x|}{x}}+{\displaystyle \frac{|y|}{y}};x=6,y=-3$

$x^y;x=16,y=-{\displaystyle \frac{1}{2}}$

${\displaystyle \frac{x^{-6}}{x^{-9}}}$

${(x^{-2})}^{-5}$

${\displaystyle \frac{x^{-3}}{y^{-2}}}$

${\left({\displaystyle \frac{x^{-3}}{y^{-1}}}\right)}^{-2}$

${\left({\displaystyle \frac{x{y}^3}{x^{5}y}}\right)}^{-2}$

${(16x^{-2/3}{y}^{-4/3})}^{3/2}$

${(49x^{-4/3}{y}^{2/3})}^{-3/2}$

${\left({\displaystyle \frac{64y^{-9/2}}{x^{-3}}}\right)}^{-2/3}$

$(2x^{2/3})(5x^{3/4})$

$(7x^{1/4})(3x^{3/2})$

${\displaystyle \frac{32x^{2/3}}{8x^{1/4}}}$

${\displaystyle \frac{x^5{(2x)}^3}{4x^3}}$

${\displaystyle \frac{{(64x^4{y}^4)}^{1/2}}{4y^2}}$

${\left({\displaystyle \frac{x^2{y}^{4/3}}{x^{1/3}}}\right)}^6$

$7\sqrt{3}+3\sqrt{75}$

${\displaystyle \frac{\sqrt{64}}{\sqrt{11}}}$

$\sqrt{180x^2}$

$7\sqrt{6}-3\sqrt{24}$

$7\sqrt[3]{54}+\sqrt[3]{128}$

$\sqrt{2x}\sqrt{6x}$

$\sqrt{75x^2}$

${\displaystyle \frac{\sqrt{100x^3}}{\sqrt{4x}}}$

$5\sqrt{2x}-2\sqrt{8x}$

$4\sqrt[3]{135}+\sqrt[3]{40}$

$y\sqrt[3]{56x}-\sqrt[3]{189x{y}^3}$

${\displaystyle \frac{7}{\sqrt{3}}}$

${\displaystyle \frac{4}{9-\sqrt{6}}}$

${\displaystyle \frac{1-\sqrt{3}}{1+\sqrt{3}}}$

${\displaystyle \frac{2\sqrt{5}+3}{3-4\sqrt{5}}}$

Write $3.7\times (6.23\times {10}^{12})$ in scientific notation.

Write ${\displaystyle \frac{3.19\times {10}^{-9}}{0.02\times {10}^{-3}}}$ in decimal notation.

$(x^3-6x^2+4x-2)+(3x^3-6x^2+5x-4)$

$(10x^3+8x^2-7x-3)-(5x^3-x^2+4x-9)$

$(4x^4+3x^3-5x^2+9)+(5x^4+8x^3-7x^2+5)$

$(8x^4+4x^3+3x^2+5)+(7x^4+3x^3+8x^2-3)$

$(x-12)(x-3)$

${(x-7)}^2$

$(x^5-2)(x^5+2)$

$(4x-3)(4x+3)$

$(2x+5)(3x-11)$

$(3x-6)(x^2+2x+4)$

$x^2-3x-10$

$x^2+10x+9$

$24x^2-38x-11$

$15x^2+33x+18$

$x(x+11)+5(x+11)$

$x^3-x^2+2x-2$

$x^4-x^3+7x-7$

$9x^2+24x+16$

$10x^2+23x+12$

$8x^2+18x+9$

$12x^2+7x-12$

$x^4-4x^2$

$4x^2-49$

$16x^2-81$

$x^2+12x+36$

$x^2-10x+100$

$64x^2+48x+9$

$8x^3-1$

$8x^3+27$

$7x^3-7$

$x^3+5x^2-16x-80$

$x^3+6x^2-9x-54$

${\displaystyle \frac{4}{x-9}}-{\displaystyle \frac{10}{9-x}}$

${\displaystyle \frac{2}{x^2-3x+2}}+{\displaystyle \frac{6}{x^2-1}}$

${\displaystyle \frac{3x+5}{x^2+14x+48}}-{\displaystyle \frac{3x-2}{x^2+10x+16}}$

${\displaystyle \frac{x+7}{x^2-7x+6}}-{\displaystyle \frac{5-3x}{x^2-2x-24}}$

${\displaystyle \frac{x-1}{x+1}}-{\displaystyle \frac{x+1}{x-1}}$

${\displaystyle \frac{x^3-1}{3x^2-3}}\cdot {\displaystyle \frac{6x+6}{x^2+x+1}}$

${\displaystyle \frac{x-1}{2x-3}}\cdot {\displaystyle \frac{4x^2-9}{2x^2-x-1}}$

${\displaystyle \frac{x^2+2x-8}{x^2+5x+6}}\cdot {\displaystyle \frac{x+2}{x+4}}$

${\displaystyle \frac{x^2-4}{4x^2-9}}\cdot {\displaystyle \frac{2x^2-3x}{2x+4}}$

${\displaystyle \frac{3x^2-17x+10}{x^2-4x-5}}\cdot {\displaystyle \frac{x^2+3x+2}{x^2+x-2}}$

${\displaystyle \frac{{\displaystyle \frac{1}{x^2}}-x}{{\displaystyle \frac{1}{x^2}}+x}}$

${\displaystyle \frac{{\displaystyle \frac{x}{x-2}}+x}{{\displaystyle \frac{1}{x^2-4}}}}$

${\displaystyle \frac{{\displaystyle \frac{x}{x-3}}+x}{{\displaystyle \frac{x}{3-x}}-x}}$

${\displaystyle \frac{x+2-{\displaystyle \frac{18}{x-5}}}{x-1-{\displaystyle \frac{12}{x-5}}}}$

Assuming that a right triangle has legs a and b of lengths 20 and 21, respectively, find the length of the hypotenuse.

One leg of a right triangle measures 5 inches. The hypotenuse is 1 inch longer than the other leg. Find the length of the hypotenuse.

Find the area A and the perimeter P of a right triangle with hypotenuse of length 20 and a leg of length 12.

Find the volume V of a box of length ${\displaystyle \frac{1}{3}},$ width 7, and height 60.

Find the area of a rectangular rug if its width is 6 feet and its diagonal measures 10 feet.

The amount of alcohol in the body of a person who drinks x grams of alcohol every hour over a relatively long period is ${\displaystyle \frac{4.2x}{10-x}}$ grams. How many grams of alcohol will be in the body of a person who drinks 2 grams of alcohol every hour (over a relatively long period)?