∑ Old Books, New Math

Chapter 27 · Irrational Equations

Chapter challenge

Ten problems drawn from every lesson in the chapter. Get each one right on your first try for a perfect score. A new set is drawn each time.

0first-try
0of 10 done

From Radicals in Formulas and Problems, exercise 42

Solve each formula for the letter named:

1

The greatest distance, x, that a ball can be thrown with velocity v (in feet per second) across a level field is given by one root of the equation .976v^2x - gx^2 = 0 (g = 32 feet). Under the conditions just stated a ball is thrown with a velocity of 100 feet per second. How far from the thrower did it strike the ground?

feet

From Radicals in Formulas and Problems, exercise 39

Solve each formula for the letter named:

2

Solve for R: \sqrt{R^2 - \left(\dfrac{R\sqrt3}{2}\right)^2} = A.

From Solving Irrational Equations, exercise 27

Solve, check results, and reject all extraneous roots:

3

\sqrt{x + 3} + \sqrt{x - 4} = \sqrt{4x - 3}

From Solving Irrational Equations, exercise 16

Solve, check results, and reject all extraneous roots:

4

\sqrt{2x + 7} = \sqrt{x} + 2

From Radicals in Formulas and Problems, exercise 41

Solve each formula for the letter named:

5

If a bullet is fired vertically, the least velocity, V, which it may have so that it will never return to the earth is given by the equation V = \sqrt{2gR} (g = 32 feet per second, R = 4000 miles). Find the velocity in miles per second to the nearest whole number.

miles per second

From Solving Irrational Equations, exercise 24

Solve, check results, and reject all extraneous roots:

6

\left(\tfrac12 + x\right)^{\frac12} = \dfrac{1 + 2x}{\left(\frac12 + x\right)^{\frac12}}

From Solving Irrational Equations, exercise 31

Solve, check results, and reject all extraneous roots:

7

\sqrt{9 - \sqrt{30 - \sqrt{20 + \sqrt{10x - 25}}}} - 2 = 0

From Solving Irrational Equations, exercise 25

Solve, check results, and reject all extraneous roots:

8

(8x)^{\frac12} - (8x - 15)^{\frac12} = \dfrac{7}{(8x - 15)^{\frac12}}

From Solving Irrational Equations, exercise 15

Solve, check results, and reject all extraneous roots:

9

\sqrt{x - 2} + \sqrt{4x + 1} = 3

From Solving Irrational Equations, exercise 3

Solve, check results, and reject all extraneous roots:

10

4\sqrt{x + 9} + 5 = 17