SQUARE ROOTSSIMPLIFYING SQUARE ROOTS

MULTIPLYING AND DIVIDING SQUARE ROOTS

ADDING AND SUBTRACTING SQUARE ROOTS

USING SQUARE ROOTS WITH THE DISTANCE FORMULA

SOLVING RADICAL EQUATIONS

SIMPLIFYING SQUARE ROOTS

•When you find the square root of a number on your calculator, you usually must round the answer.

•To get the exact answer you must simplify the square root.

•Some square roots will be a whole number answer.

•To be a whole number answer, the number you are taking the square root of will be a perfect square.

•What are some perfect squares??

SQUARE ROOTING PERFECT SQUARES

• =

• =

• =

• =

SIMPLIFYING SQUARE ROOTSHow do you find the square root of a number that is not a perfect square?

√112

• What prime factors go into 112?

• Start with 2 if the number is even.

• Divide by prime factors until you get a 1 on the left side of your line.

• This is a factor tree “stump”

256

228 214 27 71

• Circle the pairs of numbers on the right.

• Multiply the numbers in each pair together and put in front of the radical.

• Any left over numbers should be multiplied together and left under the radical.

2•2 = 4

Try a few.

Try some with variables.

Simplify the following square roots, leave all answers in radical form.

37

SIMPLIFYING SQUARE ROOTS WITH VARIABLES.

7 3 2

MULTIPLYING SQUARE ROOTS

How do you multiply square roots?• Multiply the numbers under the

radical• Simplify the square root

•

7

•

5

MULTIPLY SQUARE ROOTS WITH NUMBERS IN FRONT OF THE SQUARE ROOT• Multiply the numbers under the radical• Multiply the numbers in front of the radical• Simplify the square root

3 • 53•515

105

2 • 32•36

30

DIVIDING SQUARE ROOTS

• When dividing square roots, you must get rid of the radical in the denominator• This is called rationalizing the denominator• Multiply the numerator and denominator by the radical in the denominator• Simplify the fraction and square roots within the fraction

DIVIDE SQUARE ROOTS

• • •

= 3

ADDING SQUARE AND SUBTRACTING SQUARE ROOTS• When adding and subtracting square

roots, the radicals must be the same.• Make sure the radicals have the same

number.• Add or subtract the number in front of the

radical, but leave the radical and what’s in it alone.• If the numbers inside the radical are not

the same then you can not put them together.• Adding and subtracting square roots is like

adding and subtracting like terms.

ADDING AND SUBTRACTING SQUARE ROOTS9 - 15 23 + 33 -6

56

-4 - 10 -2 + 3 - 5 -12 - 10 -2 + 9 - 5 -22 7 - 5

TRY SOME PROBLEMS

-3 - 9

25 + 3

3 - 5

3 - 5 + 7

APPLYING SQUARE ROOTS USING THE DISTANCE FORMULA

d =

(3, -2), (5, 3)d = d = d = d =

(9, 4), (4, -2)d = d = d = d =

WHAT IS THE DISTANCE BETWEEN THESE POINTS??

(4, 7), (9, 3)

(-2, -4), (-6, 3)

(10, -3), (15, 2)

(5, 4), (5, -3)

SOLVING RADICAL EQUATIONS

• When solving radical equations you want to try to get rid of the square roots.• You can square both sides of the

equation to get rid of the square root.• After the square root is gone, then

solve the equation for the given variable.

SOLVE THE FOLLOWING RADICAL EQUATIONS

= 5 = 10 4 =

2 = 22 - 5 = 3 =