ROOTS,POWERS,& SCIENTIFIC NOTATION
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Perfect squares and Perfect cubes and their Roots
A perfect cube is a integer that can be multiplied by itself three times to get a rational number.An example can be 3 again. if 3 is multiplied bye itself 3 times you get 27.
If you have a square root you would fine a number that can be multiplied by itself to get an integer. So if you asked what the square root of 9 it would be 3 because 3 times 3 is 9.
If you have a cubed root you would find a number that can be multiplied by it self three times to find an integer. So if you say what is the cubed root of 27 it would be 3 because 3 times 3 is 9. Then nine times 3 is 27
A non perfect square is a number that does not produce an integer when one takes the square root of it. An example 10 the square root of ten is 3.0622. So 10 is not a perfect square.
To find a non-perfect square you would find the closest perfect squares to it. So lets say the square root of ten. this is between 3(which is 9) and 4(which is 16). So you would probably start with 3.5 which is 12.25 which is high. Then maybe you would try 3.2 which is 10.24. You would eventually end up at 3.16227766.
All the power rules
These are the different ways you can simplify exponents.
Product: Keep base and add the exponents.
Quotient: Keep the base and subtract the exponent.
Power of a Power: Keep the base multiply the exponents
Negative Exponents: Move the number and the negative exponent to denominator and put a 1 over it and make the exponent positive
Zero Exponents: Any number raised to the zero power equals one
it will run 30 miles
The reason we use it
How to do it
You can also convert them back to standard notation by doing the opposite
Different ways to do it
Add: If the number is a decimal you would move the decimal to make the number between 1 and 10 then add how ever many decimal places you moved the decimal, to the exponent.
Multiply:To multiply two numbers expressed in scientific notation,
simply multiply the numbers out front and add the exponents.
(n x 10a) • (m x 10b) = (n · m) x 10a+b
Divide:To divide two numbers expressed in scientific notation,
simply divide the numbers out front and subtract the exponents.
Answer is 5.75x10^5