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Squares,Square Roots, Cubes, Cube roots
These instructions cover the use of:
- B ( or A ) to find squares and square roots
- K to find cubes and cube roots
- R1 and R2 to find high precision squares and square roots
- Q1,Q2 and Q3 to find high precision cubes and cube roots
It's pretty easy to glance at the B and C scales and go "right, square root of 9 is 3." The difficulties arise only in setting the decimal points and interpreting the duplicate nature of these scales. This tutorial addresses those difficulties in a step by step manner. For many problems, you'll have an idea of what the answer will be, and you won't need to bother. These instructions will allow you to correctly evaluate operations on very large and small numbers, where you are at a loss as to what the answer should look like. Learn to do squares and roots with the B scale first. The other instructions for A,K,R1-2,Q1-3 are all analogous.
Terminology
In our discussion, we will always assume the C,D,R,Q scales run from 1 to 10. We will refer to numeric positions as decimal numbers between 1 and 10. Likewise, A and B will be written as running from 1 to 100, and the K scale from 1 to 1000.
To find y = x squared, if x is on C:
- set cursor at xC,
- read coefficient of y on B.
- Assign the decimal point.
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To find y = x squared, if x is on D:
- set cursor at xD
- read coefficient of y on A
- Assign the decimal point.
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Examples
- 5 squared
- Set cursor at 5C, read 25 on B. Decimal is correct.
- OR Set cursor at 5D, read 25 on A. Decimal is correct.
- 2455 squared
- Set cursor at 2.455C, read 6.027 on B.
- set decimal as described in tutorial: 2455->2.455E3 -> 3*2 = 6 -> answer 6.027E6, about 6 million.
to find y = sqrt(x), if x is on B:
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to find y = sqrt(x), if x is on A:
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This is just the opposite of the procedure for squaring. For instance the pictoral example of 5 squared could just as easily be titled "Square root of 25".
Examples
- square root of 36
- 36 is on the right (10..100) decade.
- Set cursor at 36B, read 6 on C. Decimal is correct.
- square root of 2455
- 2455 is 2.455E3, 3 is odd, so use the right (10..100) decade.
- Set cursor at 24.55B, read 4.955 on C.
- set decimal as described in tutorial: floor(3/2) is 1, so answer is 4.955E1, 49.55
Examples:
- 14 cubed
- Set cursor at 1.4D, read 2.744 on K. Exponent: 14 is 1.4E1, 1*3 = 3. Answer 2.744E3 : 2744.
- The above diagram doesn't show much precision, but remember that with zooming, you can get a much better value, in this case the exact value.
- 2455 cubed
- Set cursor at 2.455D, read 14.80 on K.
- set decimal as described in tutorial: 2455->2.455E3 -> 3*3 = 9 -> answer 14.80E9,1.480E10 about 15 Billion.
- 0.5 cubed
- Set cursor at 5D, read 125 on K
- set decimal as descrived in tutorial: 0.5 -> 5E-1. -1*3 = -3. Answer 125E-3 = 1.25E-1 = 0.125
Examples
- cube root of 14
- Set cursor at 1.4C, read 2.744 on K. Exponent: 14 is 1.4E1, 1*3 = 3. Answer 2.744E3 : 2744.
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- the above diagram doesn't show much precision, but remember that with zooming, you can get this exact value
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- cube root of 2455
- Set cursor at 2.455C, read 14.80 on K.
- set decimal as described in tutorial: 2455->2.455E3 -> 3*3 = 9 -> answer 14.80E9,1.480E10 about 15 Billion.
- cube root of 0.5
- Set cursor at 5C, read 125 on K
- set decimal as described in tutorial: 0.5 -> 5E-1. -1*3 = -3. Answer 125E-3 = 1.25E-1 = 0.125
These instructions assume R1,R2 are both on the stock. If they're on the slider, just use C instead of D.
to find y = x squared:
- find x on R1 or R2 (wherever it's found)
- read the coefficient of y on D
- Assign the decimal point.
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Compared with finding squares with A, this is reversed. You find your value on R, and read the square on D.
Example
- square of 0.0282
- set cursor at 2.82 on R1
- read coefficient of answer on D: 7.95
- set the decimal: 0.0282 is 2.82E-2. -2*2=-4; Answer is 7.95E-4 , 0.000795
These instructions assume R1,R2 are both on the stock. If they're on the slider, just use C instead of D.
Compared with finding square roots with A, this is reversed. You find your value on D, and read the square root on R1/R2.
Examples
- square root of 170000
- set cursor at 1.7 on D
- use R2 because exponent of 1.7E5 is odd
- read coefficient of answer on R2: 4.12
- set the decimal: exponent is 5, floor(5/2)=2; Answer is 4.12E2, 412.
These instructions assume the Q scales are all the stock. If they're on the slider, just use C instead of D.
to find y = x cubed:
- find x on Q1,Q2 or Q3 (wherever it's found)
- read the coefficient of y on D
- Assign the decimal point.
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Compared with finding cubes with K, this is reversed. You find your value on Q, and read the cube on D.
Example
- cube of 0.0282
- set cursor at 2.82 on Q2
- read coefficient of answer on D: 2.243
- set the decimal: 0.0282 is 2.82E-2. -2*3=-6; Answer is 2.243E-6, 0.000002243
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These instructions assume the Q are both on the stock. If they're on the slider, just use C instead of D.
Compared with finding cube roots with K, this is reversed. You find your value on D, and read the cube root on a Q scale.
Examples
- cube root of 170000 (1.7E5)
- set cursor at 1.7 on D
- use Q3 because you have to reduce exponent 5 twice before 3 divides it.
- read coefficient of answer on Q3: 5.54
- set the decimal: exponent is 5, floor(5/3)=1; Answer is 5.54E1, 55.4.
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