REVIEW OVER RADICALS/ROOTS

OBJECTIVE FOR THE DAY

• Review over fractional exponents
• Review over inverse operations
• Go over roots
• Review over some rules for roots
• Simplify roots
• Examples
• Now try some on your own!

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REVIEW

What is an exponent?

An easy way to write a single number being multiplied, multiple times.

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What is the base of an exponent?

The base is the number being multiplied

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What is the exponent?

The number of times the base is multiplied

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How do we multiply exponents?

If they have the same base, we add the exponents together.

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How do we divide exponents?

If they have the same base, we subtract the top exponent from the bottom exponent.

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Quick review on fractional exponents

A fractional exponent is an exponent, taken to a power that happens to be a fraction.

The denominator of the fraction tells us how many times we are to break up the base.

The numerator of the fractions tells us how many times we need to multiply the broken pieces together to get the answer.

So, for example:

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3 3 3

Another example of fractional exponents

2 2 2 2 2 2

So, then what are roots?

A root is simply another way to write a fractional exponent.

The reason you are being taught roots, is because almost NO ONE uses fractional exponents if they can help it.

(No one like fractions, not even mathematicians and physicists.)

Instead, we use roots to solve because they are easier to work with.

So, here is what a root is.

An explanation of roots

Explanation of roots importance

This is important because this is the inverse operation to exponential expressions.

Remember, an inverse operation is the opposite operation to another operation.

An example of this is subtraction.

The opposite of subtraction is….

Addition.

So they are inverse operations.

Same with multiplication. The inverse to multiplication is…..

Division.

So what’s the inverse operation to exponential expressions?

Roots.

SO WHAT DOES THIS ALL MEAN?

9,-9 = x

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So what did we just do there?

We took the root of each side of the equation (because what you do to one side, you need to do to another).

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A FEW RULES

YOU CAN ALSO BREAK SQUARE ROOTS

SIMPLIFIED PROPERLY

EXAMPLE 1

So now we divide the equation by x and we get:

x = -9,9

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So now we can solve exponential equations much easier.

EXAMPLE 2

EXAMPLE 3

Now try some on your own!

Surprise! It’s you other homework, nothing new.