Let’s get Radical

The symbol for square root, √, called a radical sign, denotes the principal or nonnegative square root.

The expression under the radical sign is called the radicand.

Therefore: The square root of a negative number is not a real number.

No number squared equals a negative product. Example: √-25 has no real number solution.

However, , since the negative sign is outside the radical sign.

Quotient Property of Square Roots

Simplifying Square Roots

8

We can simplify if 8 contains a Perfect Square

Simplifying Square Roots

8

4 2

2 2

Look to factor perfect squares (4, 9, 16, 25, 36…)

Put perfect squares in first radical and the other factor in 2nd.

Take square root of first radical

Simplifying Square Roots

48

16 3

4 3

Factor any perfect squares (4, 9, 16, 25, x2, y6…)

(& Put perfect squares in first radical and other factor in 2nd)

Take square root of first radical

Simplifying Square Roots

27x 2

9x 2 3

3x 3

Factor any perfect squares (4, 9, 16, 25, 36…)

(& Put perfect squares in first radical and other factor in 2nd)

Take square root of first radical

Simplifying Radicals

100x 2 2x

Remember:

Factor any perfect squares (4, 9, 16, 25, 36…)

(& Put perfect squares in first radical and other factor in 2nd)

200x 3

100x 2 2x

10x 2x

Take square root of first radical

200x 3 Simplifying Radicals

Time for a“Mental Math”

Break!

Welcome to“Make That Number”

Using the numbers

5, 4, 8

in any order and any combination of multiplication, division, subtraction and/or addition, make the following

number:

12

5 × 4 - 8

Using the numbers

8, 6, 9 in any order and any combination of multiplication, division, subtraction and/or addition, make the following

number:

62

8 + 6 × 9

Now back to our regularly scheduled slideshow!

Factor any perfect squares (4, 9, 16, 25, x2, y6…) from NUMERATOR & DENOM.

(& Put perfect squares in first radical and other factor in 2nd)

200x 3

25

Simplifying Fraction Radicals

100x 2 2x

10x 2x

25 5

200x 3

Factor any perfect squares (4, 9, 16, 25, x2, y6…) from NUMERATOR & DENOM.

(& Put perfect squares in first radical and other factor in 2nd)

Take square root of first radical

200x 3

25

Simplifying Fraction Radicals

100x 2 2x

10x 2x

25 5

200x 3

10x 2x

5

1. Factor any perfect squares (4, 9, 16, 25, x2, y6…) from NUMERATOR & DENOM.

(& Put perfect squares in first radical and other factor in 2nd)

2. Take square root of first radical

3. REDUCE

200x 3

25

Simplifying Fraction Radicals

100x 2 2x

10x 2x

25 5

200x 3

10x 2x

5

2x 2x

Classwork/Homework

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.