Chapter 1: Fundamentals

Rationalize the denominator.

$\frac{2}{\sqrt{2}+\sqrt{7}}$

Factor the expression by grouping terms

$18x^3+9x^2+2x+1$

Write the number indicated in each statement in scientific notation.

1. The distance from the earth to the sun is about 93 million miles.
2. The mass of an oxygen molecule is about $0.000000000000000000053g$
3. The mass of the earth is about $5,970,000,000,000,000,000,000,000kg$.

Rationalize the denominator.

$\frac{1}{\sqrt{x}+1}$

Find the real solutions of the quadratic equation $\frac{1}{x-1}-\frac{2}{x^2}=0$.

Solve the absolute value Inequality. Express the answer using interval notation and graph the solution set.

$3-|2x+4|\le 1$

Find the center and radius of the circle, and sketch its graph.

${\left(x+1\right)}^2+{\left(y+2\right)}^2=36$

Solve the inequality $\mathbf{-}\mathbf{1}\mathbf{<}\mathbf{2}\mathbf{x}\mathbf{+}\mathbf{5}\le \mathbf{3}$, express the solution using interval notation and graph the solution set on real number line.

Explain why the sum, the difference, and the product of two rational numbers are rational numbers. Is the product of two irrational numbers necessarily irrational? What about the sum?

Two computer monitors sitting side by side on a shelf in an appliance store have the same screen height. One has a screen that is7in. wider than it is high. The other has a wider screen that is1.8times as wide as it is high. The diagonal measure of the wider screen is3in. more than the diagonal measure of the smaller screen. What is the height of the screens, correct to the nearest0.1in.?