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 We can simplify if 8 contains a Perfect Square

Simplifying Square Roots 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 Factor any perfect squares (4, 9, 16, 25, x 2, y 6 …) (& Put perfect squares in first radical and other factor in 2nd) Take square root of first radical

Simplifying Square Roots 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 Remember: 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

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, x 2, y 6 …) from NUMERATOR & DENOM. (& Put perfect squares in first radical and other factor in 2nd) Simplifying Fraction Radicals

Factor any perfect squares (4, 9, 16, 25, x 2, y 6 …) from NUMERATOR & DENOM. (& Put perfect squares in first radical and other factor in 2nd) Take square root of first radical Simplifying Fraction Radicals

1. Factor any perfect squares (4, 9, 16, 25, x 2, y 6 …) from NUMERATOR & DENOM. (& Put perfect squares in first radical and other factor in 2nd) 2. Take square root of first radical 3. REDUCE Simplifying Fraction Radicals

Classwork/Homework