ROOTS,POWERS,& SCIENTIFIC NOTATION

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ROOTS

Perfect squares and Perfect cubes and their Roots

A perfect square is an integer that can be multiplied by itself.Example 3 is a perfect square because it can be multiplied by itself to get 9.

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

Word Problem

If Jimmy has a fenced in yard and it is 25 sq. ft. what is the length of each side of the fence in square root form.The answer is 5 because 5 times 5 is 25

Non-Perfect Square

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.

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Powers

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

Word Problem

If a cat runs at 10mph how far will it run in 3 hours.

it will run 30 miles

Scienific Notation

The reason we use it

We use it to convert really small and large numbers to numbers we can understand.

How to do it

To convert a big or small number into a number that is greater than 1 but less than 10, you have to move the decimal to the right or the left. Small numbers have a negative exponent and large numbers have a positive exponents. Then when you have the number in scientific notion you would multiply it by ten to the power of decimal places you move the decimal.

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.

15.97x10^14=1.597x10^15


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.

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This above picture is subtracting
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this above picture is dividing

Word Problem

Say your yard is 6.9x10^6 and your garden is 0.12x10^2. How many gardens can u fit in your yard.(hint:divide)

Answer is 5.75x10^5