Math Is Fun Forum

Rationalize Denominator

Let cb = cube root

5/[cr{2}]

I multiplied the top and bottom by [cr{2}].

After doing that I ended up with (5•cr{2})/2 as my final answer.

The book's answer is (5•cr{4})/2.

Where did 4 come from?

Plot the given points. Then plot the points that are symmetric to the original points with respect to the x-axis, y-axis or the origin.

Given points: (5, 3), (4, -2)

Let me see.

I will not show the plotting of the points because this requires a graph, which means a picture. I have not been able to upload photos to the site.

Symmetric with respect to the x-axis:

(5, 3) ==> (5, -3)

(4, -2) ==> (4, 2)

Symmetric with respect to the y-axis:

(5, 3) ==> (-5, 3)

(4, -2) ==> (-4, -2)

Symmetric with respect to the origin:

(5, 3) ==> (-5, -3)

(4, -2) ==> (-4, 2)

You say?

Verify that the points (0, 0), (a, 0), and (a/2, sqrt{3}a/2) are the vertices of an equilateral triangle. Then show that the midpoint of the three sides are the vertices of a second equilateral triangle.

Any hints?

Overlay a rectangular coordinate system on a Little League baseball diamond so that the origin is at home plate, the positive  x-axis lies in the direction from home plate to first base, and the positive y-axis lies in the direction from home plate to third base.

A. What are the coordinates of first base, second base, and third base?

B.if the right fielder is located at (180, 20), how far is it from the right fielder to second base?

C. If the center fielder is located at (220, 220), how far is it from the center fielder to third base?

NOTE: THE BASES ARE SEPARATED BY 90 FEET AROUND THE BASEBALL DIAMOND.

Let me see.

For A:

First base coordinates (90, 0).

Second base coordinates (90, 90).

Third base coordinates (0, 90).

You say?

For B:

Let R = distance from right field to second base.

R = sqrt{(180 - 90)^2 + (20 - 90)^2}

Is this correct?

For C:

Let C = distance from center field to third base.

C = sqrt{(220 - 0)^2 + (220 - 90)^2}

You say?

Suzanne Somers of Three's Company and Step By Step dead at 76. She was beautiful, sexy, smart and funny. Thank you, Suzanne Somers for the laughs.

The medians of a triangle are the line segments from each vertex to the midpoint of the opposite side. Find the lengths of the medians of triangle ABC with vertices at A = (0, 0), B = (6, 0), and C = (4, 4).

Let me see.

The author gave no sample question for this problem.

I think this is what I must do:

1. Find the midpoint of line segments AB, BC, and AC.

2. I then must use the distance formula for points to find the following:

A. Distance form point A to the midpoint of BC.

B. Distance from point B to the midpoint AC.

C. Distance from point C to the midpoint AB.

You say?