Chapter 1

Mass of an electron The mass of an electron is approximately \(9.1 \times 10^{-31}\) kilogram. Express this number in decimal form.

Factor the polynomial. $$ x^{2}+3 x+4 $$

Exer. 53-56: Rewrite the expression using a radical. (a) \(8-y^{1 / 3}\) (b) \((8-y)^{1 / 3}\)

Light year In astronomy, distances to stars are measured in light years. One light year is the distance a ray of light travels in one year. If the speed of light is approximately 186,000 miles per second, estimate the number of miles in one light year.

Factor the polynomial. $$ 3 x^{2}-4 x+2 $$

Exer. 53-56: Rewrite the expression using a radical. (a) \(8 y^{1 / 3}\) (b) \((8 y)^{1 / 3}\)

Factor the polynomial. $$ 6 x^{2}+7 x-20 $$

Exer. 57-80: Simplify the expression, and rationalize the denominator when appropriate. $$ \sqrt{81} $$

Avogadro's number The number of hydrogen atoms in a mole is Avogadro's number, \(6.02 \times 10^{23}\). If one mole of the gas has a mass of \(1.01\) grams, estimate the mass of a hydrogen atom.

Factor the polynomial. $$ 12 x^{2}-x-6 $$

Exer. 57-80: Simplify the expression, and rationalize the denominator when appropriate. $$ \sqrt[3]{-125} $$

Fish population The population dynamics of many fish are characterized by extremely high fertility rates among adults and very low survival rates among the young. A mature halibut may lay as many as \(2.5\) million eggs, but only \(0.00035 \%\) of the offspring survive to the age of 3 years. Use scientific form to approximate the number of offspring that live to age 3 .

Factor the polynomial. $$ 12 x^{2}-29 x+15 $$

Exer. 57-80: Simplify the expression, and rationalize the denominator when appropriate. $$ \sqrt[5]{-64} $$

Frames in a movie film One of the longest movies ever made is a 1970 British film that runs for 48 hours. Assuming that the film speed is 24 frames per second, approximate the total number of frames in this film. Express your answer in scientific form.

Factor the polynomial. $$ 21 x^{2}+41 x+10 $$

Exer. 57-80: Simplify the expression, and rationalize the denominator when appropriate. $$ \sqrt[4]{256} $$

Large prime numbers The number \(2^{44,497}-1\) is prime. At the time that this number was determined to be prime, it took one of the world's fastest computers about 60 days to verify that it was prime. This computer was capable of performing \(2 \times 10^{11}\) calculations per second. Use scientific form to estimate the number of calculations needed to perform this computation. (More recently, in \(2005,2^{30,402,457}-1\), a number containing \(9,152,052\) digits, was shown to be prime.)

Factor the polynomial. $$ 4 x^{2}-20 x+25 $$

Exer. 57-80: Simplify the expression, and rationalize the denominator when appropriate. $$ \frac{1}{\sqrt[3]{2}} $$

Tornado pressure When a tornado passes near a building, there is a rapid drop in the outdoor pressure and the indoor pressure does not have time to change. The resulting difference is capable of causing an outward pressure of \(1.4 \mathrm{lb} / \mathrm{in}^{2}\) on the walls and ceiling of the building. (a) Calculate the force in pounds exerted on 1 square foot of a wall. (b) Estimate the tons of force exerted on a wall that is 8 feet high and 40 feet wide.

Factor the polynomial. $$ 9 x^{2}+24 x+16 $$

Exer. 57-80: Simplify the expression, and rationalize the denominator when appropriate. $$ \sqrt{\frac{1}{7}} $$

Cattle population A rancher has 750 head of cattle consisting of 400 adults (aged 2 or more years), 150 yearlings, and 200 calves. The following information is known about this particular species. Each spring an adult female gives birth to a single calf, and \(75 \%\) of these calves will survive the first year. The yearly survival percentages for yearlings and adults are \(80 \%\) and \(90 \%\), respectively. The male-female ratio is one in all age classes. Estimate the population of each age class (a) next spring (b) last spring

Factor the polynomial. $$ 25 z^{2}+30 z+9 $$

Exer. 57-80: Simplify the expression, and rationalize the denominator when appropriate. $$ \sqrt{9 x^{-4} y^{6}} $$

Factor the polynomial. $$ 16 z^{2}-56 z+49 $$

Exer. 57-80: Simplify the expression, and rationalize the denominator when appropriate. $$ \sqrt{16 a^{8} b^{-2}} $$

Factor the polynomial. $$ 45 x^{2}+38 x y+8 y^{2} $$

Exer. 57-80: Simplify the expression, and rationalize the denominator when appropriate. $$ \sqrt[3]{8 a^{6} b^{-3}} $$

Factor the polynomial. $$ 50 x^{2}+45 x y-18 y^{2} $$

Exer. 57-80: Simplify the expression, and rationalize the denominator when appropriate. $$ \sqrt[4]{81 r^{5} s^{8}} $$

Factor the polynomial. $$ 36 r^{2}-25 t^{2} $$

Exer. 57-80: Simplify the expression, and rationalize the denominator when appropriate. $$ \sqrt{\frac{3 x}{2 y^{3}}} $$

Factor the polynomial. $$ 81 r^{2}-16 t^{2} $$

Exer. 57-80: Simplify the expression, and rationalize the denominator when appropriate. $$ \sqrt{\frac{1}{3 x^{3} y}} $$

Factor the polynomial. $$ z^{4}-64 w^{2} $$

Exer. 57-80: Simplify the expression, and rationalize the denominator when appropriate. $$ \sqrt[3]{\frac{2 x^{4} y^{4}}{9 x}} $$

Factor the polynomial. $$ 9 y^{4}-121 x^{2} $$

Exer. 57-80: Simplify the expression, and rationalize the denominator when appropriate. $$ \sqrt[3]{\frac{3 x^{2} y^{5}}{4 x}} $$

Factor the polynomial. $$ x^{4}-4 x^{2} $$

Exer. 57-80: Simplify the expression, and rationalize the denominator when appropriate. $$ \sqrt[4]{\frac{5 x^{8} y^{3}}{27 x^{2}}} $$

Factor the polynomial. $$ x^{3}-25 x $$

Exer. 57-80: Simplify the expression, and rationalize the denominator when appropriate. $$ \sqrt[4]{\frac{x^{7} y^{12}}{125 x}} $$

Factor the polynomial. $$ x^{2}+25 $$

Exer. 57-80: Simplify the expression, and rationalize the denominator when appropriate. $$ \sqrt[5]{\frac{5 x^{7} y^{2}}{8 x^{3}}} $$

Factor the polynomial. $$ 4 x^{2}+9 $$

Exer. 57-80: Simplify the expression, and rationalize the denominator when appropriate. $$ \sqrt[5]{\frac{3 x^{11} y^{3}}{9 x^{2}}} $$

Factor the polynomial. $$ 75 x^{2}-48 y^{2} $$

Exer. 57-80: Simplify the expression, and rationalize the denominator when appropriate. $$ \sqrt[4]{\left(3 x^{5} y^{-2}\right)^{4}} $$