Radical (Square Roots)

Algebra I

What is a radical?

• An expression that uses a root, such as square root, cube root

Finding a square or cube root

• Use your calculator – The square root function – The math function, option #4 for cubed

Simplifying Radicals

• For every pair, you take out one as a whole number.

Simplifying Radicals

• When the square root isn’t a perfect square there are different ways to simplify.– Put the value in the calculator, get the

decimal value and round.– Simplify keeping the answer in radical

form.– Fractions separate the top and the

bottom

Simplifying Radicals

• Fraction square roots – separate the numerator and the denominator, find each square root, then reduce if necessary.

Simplifying Radicals

• Find the prime factors of the numbers or variables under the radical.

24 8 3 4 2 2 2

Simplifying Radicals

• Find the prime factors of the numbers or variables under the radical.

24 8 3 4 2 2 2

Simplifying Radicals

• Find the prime factors of the numbers or variables under the radical.

24 8 3 4 2• Find pairs 2 2

Simplifying Radicals

• Find the prime factors of the numbers or variables under the radical.

• Find pairs • Take one out of the radical and leave the

rest under the radical.

2

Simplifying Radicals

• Find the prime factors of the numbers or variables under the radical.

• Find pairs • Take one out of the radical and leave the rest

under the radical.

2• Multiply the numbers inside the radical.

2

Simplifying Radicals

Simplifying Radicals

Simplifying Radicals

• Now you try…

Simplifying Radicals

Finding Area and Volume Using Radicals

• Find the area of this rectangle. A = lw

Finding Area and Volume Using Radicals

• Find the area of this rectangle. A = lw A = ( )( )

Finding Area and Volume Using Radicals

• Find the area of this rectangle. A = lw A = ( )( ) = 15

Finding Area and Volume Using Radicals

• Find the length of the sides of this square.

A = s² A = 225ft²

Finding Area and Volume Using Radicals

• Find the length of the sides of this square.

A = s² A = 225ft²• Find the square root of the area.

= 15

Finding Area and Volume Using Radicals

• Find the length of the sides of this cube.

V = lwh V = 125ft³

Finding Area and Volume Using Radicals

• Find the length of the sides of this cube.

V = lwh V = 125ft³Find the cube root of the volume.

Finding Area and Volume Using Radicals

• Find the length of the sides of this cube.

V = lwh V = 125ft³Find the cube root of the volume.

= 5