Working With Radicals

Do Now Simplify each of the exponential expressions

You know these rules

Let’s look at how we can work with expressions such as

Open the TI-NSPIRE FileTI-NSPIRE Let’s look at some table values for x 1/2. Look for some special values you might recognize. What would be another way to express x 1/2 ? Look at a graph and click on the line to see what graph has been plotted.

Some things your observed How can you rewrite each of the following with a fractional exponent?

So we know that

Open the TI-NSPIRE FileTI-NSPIRE Let’s look at some table values for x 1/3. Look for some special values you might recognize. What would be another way to express x 1/3 ? Look at a graph and click on the line to see what graph has been plotted.

Some things your observed How can you rewrite each of the following with a fractional exponent?

So we know that

Open the TI-NSPIRE FileTI-NSPIRE Let’s look at some table values for x 1/4. Look for some special values you might recognize. What would be another way to express x 1/3 ? Look at a graph and click on the line to see what graph has been plotted.

Some things your observed How can you rewrite each of the following with a fractional exponent?

So we know that

Which problems can you rewrite? Now let’s find out how we look at the others!

Open the TI-NSPIRE FileTI-NSPIRE Let’s look at some table values for 4 x, such as 4 1, 4 1.5, 4 2, 4 2.5, 4 3, 4 3.5, 4 4, etc. Look for some special values you might recognize like 4 1, 4 2, 4 3, 4 4. Look at the value for x = 1.5. Remember this is What fractional power could replace 1.5?

To find a value for we need to do a little math.

Look at x = 2.5

Try changing

Open the TI-NSPIRE FileTI-NSPIRE Let’s look at some table values for 16 x, such as 16 1, , 16 2, , 16 3, , 16 4, etc. Look for some special values you might recognize. First look at 16 1, 16 2, 16 3 Look at the value for x = What fraction could replace 1.25?

Simplify

So how could we rewrite

Simplify each expression:

Now can you simplify the rest?

Simplify these

Using the new ideas to solve equations These statements state that the cube root of some number is 4. What operation will undo the cube root? We’ll cube both sides. Our solution checks

Solve this equation These statements are the same. How can we undo raising a number to the 4/3 power? We’ll raise each side to the ¾ power Our solution checks

Solve this equation These statements are the same. How can we undo raising a number to the 4/3 power? We’ll raise each side to the power of 4 Our solution checks

Solve this equation These statements are the same. How can we undo raising a number to the 4/3 power? We’ll raise each side to the power of 3 Our solution checks