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101 lines
2.2 KiB
Markdown
101 lines
2.2 KiB
Markdown
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The [SQR](SQR) function returns the square root of a numerical value.
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## Syntax
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> square_root = [SQR](SQR)(value)
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## Description
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* The *square root* returned is normally a [SINGLE](SINGLE) or [DOUBLE](DOUBLE) numerical value.
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* The *value* parameter can be any **positive** numerical type. **Negative parameter values will not work!**
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* Other exponential root functions can use fractional exponents([^](^)) enclosed in **parenthesis only**. EX: root = c ^ (a / b)
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## Example(s)
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Finding the hypotenuse of a right triangle:
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```vb
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A% = 3: B% = 4
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PRINT "hypotenuse! ="; SQR((A% ^ 2) + (B% ^ 2))
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```
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```text
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hypotenuse = 5
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```
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Finding the Cube root of a number.
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```vb
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number = 8
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cuberoot = number ^ (1/3)
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PRINT cuberoot
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```
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```text
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2
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```
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Negative roots return fractional values of one.
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```vb
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number = 8
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negroot = number ^ -2
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PRINT negroot
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```
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```text
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.015625
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```
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> *Explanation:* A negative root means that the exponent value is actually inverted to a fraction of 1. So x ^ -2 actually means the result will be: 1 / (x ^ 2).
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Fast Prime number checker limits the numbers checked to the square root (half way).
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```vb
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DEFLNG P
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DO
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PRIME = -1 'set PRIME as True
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INPUT "Enter any number to check up to 2 million (Enter quits): ", guess$
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PR = VAL(guess$)
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IF PR MOD 2 THEN 'check for even number
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FOR P = 3 TO SQR(PR) STEP 2 'largest number that could be a multiple is the SQR
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IF PR MOD P = 0 THEN PRIME = 0: EXIT FOR 'MOD = 0 when evenly divisible by another
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NEXT
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ELSE : PRIME = 0 'number to be checked is even so it cannot be a prime
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END IF
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IF PR = 2 THEN PRIME = -1 '2 is the ONLY even prime
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IF PR = 1 THEN PRIME = 0 'MOD returns true but 1 is not a prime by definition
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IF PRIME THEN PRINT "PRIME! How'd you find me? " ELSE PRINT "Not a prime, you lose!"
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LOOP UNTIL PR = 0
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```
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```text
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Enter any number to check up to 2 million (Enter quits): 12379
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PRIME! How'd you find me?
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```
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*Note:* Prime numbers cannot be evenly divided by any other number except one.
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## See Also
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* [MOD](MOD) (integer remainder division)
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* [^](^) (exponential operator)
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* [Mathematical Operations](Mathematical-Operations)
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* [Mathematical Operations](Mathematical-Operations)
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