Miscellaneous

Elementary
GCD
LCM
Definitions

Percents

Ratios

Square Roots

Reverses

Junior High
Cube Roots

Mult By 9 (#1)
Mult By 9 (#2)

Mult By 8

Polynomials

Positive Integral Divisors

Sum Of Positive Integral Divisors

Relatively Prime 

Triangular Numbers

Remainders

Divide By 40

Divide By 25

Divide By 9

High School

Pentagonal Numbers

Hexagonal Numbers

Heptagonal Numbers

Octagonal Numbers

Manipulating Polygonal Numbers

Dividing Factorials #1

Dividing Factorials #2

Solving Triangular Numbers

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Cube Roots:

A.  Working with cube roots is very similar to working with square roots.

1.  By looking at the last number, we can determine the last digit of the answer.

If the last number ends in:

0 -> the last digit ends in 0.

1 -> the last digit ends in 1.

2 -> the last digit ends in 8.

3 -> the last digit ends in 7.

4 -> the last digit ends in 4.

5 -> the last digit ends in 5.

6 -> the last digit ends in 6.

7 -> the last digit ends in 3.

8 -> the last digit ends in 2.

9 -> the last digit ends in 9.

2.  Once the last digit is determined, write it down and mentally chop off the last 3 digits under the cube root.

3.  Using your knowledge of cubes, find what numbers the remaining are between.  Write the smallest of these numbers.

Ex [1]  ³/(373248) = __________.

a.  We know the last digit ends in a 2.  Write 2.

b.  Chopping off the last 3 numbers we are left with 373.

c.  We know that 7³ = 343 and 8³ = 512, so the first digit is 7.  Write 7.

d.  The answer is 72.

Ex [2]  ³/(1601613) = __________.

a.  We know that the last digit is 7.  Write 7.

b.  Chopping off the last 3 digits we are left with 1601.

c.  We know that 11³ = 1331 and 12³ = 1728, so the first digits are 11.  Write 11.

d.  The answer is 117.

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