Transcript Square Roots

SQUARE ROOTS
SIMPLIFYING 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
•
225 =
•
100 =
•
36 =
•
625 =
•
81 =
SIMPLIFYING SQUARE ROOTS
How do you find the square root of a number that is not a
perfect square?
• What prime factors go into 112?
112
56
28
14
7
1
2
2
2
2
7
2•2 7 = 4 7
• 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”
• 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.
Try a few.
288
216
280
Try some with variables.
216𝑛2
147𝑎3 𝑏 2
216𝑐 7
Simplify the following square roots, leave all answers
in radical form.
4 108
3 294
7 605
SIMPLIFYING SQUARE ROOTS WITH VARIABLES.
98𝑥 2
360𝑛5
500𝑥 6
7 84𝑚7
3 450𝑥 8
2 288𝑡 3
MULTIPLYING SQUARE ROOTS
How do you multiply square roots?
• Multiply the numbers under the radical
• Simplify the square root
7• 7
49
7
5 • 15
75
5 3
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 7 • 5 21
3•5 7 • 21
15 147
105 3
2 10 • 3 15
2•3 10 • 15
6 150
30 6
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
35
5
•
175
5
5 7
5
7
5
5
3
5
•
3 5
5
5
5
3 20
2 5
•
3 100
2•5
3 • 10
10
30
=3
10
5
5
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 ROOTS
9 7 - 15 7
-6 7
23 5 + 33 5
56 5
-4 45 - 10 5
-12 5 - 10 5
-22 5
-2 3 + 3 27 - 5 5
-2 3 + 9 3 - 5 5
7 3-5 5
TRY SOME PROBLEMS
-3 15 - 9 15
3 3 - 5 27
25 6 + 3 24
3 18 - 5 12 + 7 18
APPLYING SQUARE ROOTS USING THE DISTANCE
FORMULA
d=
d=
d=
d=
d=
(𝑥1 − 𝑥2 )2 + (𝑦1 − 𝑦2 )2
(3, -2), (5, 3)
(3 − 5)2 +(−2 − 3)2
(−2)2 +(−5)2
4 + 25
29
(9, 4), (4, -2)
d = (9 − 4)2 +(4 − (−2))2
d = (5)2 +(6)2
d = 25 + 36
d = 61
WHAT IS THE DISTANCE BETWEEN THESE POINTS??
(4, 7), (9, 3)
(10, -3), (15, 2)
(-2, -4), (-6, 3)
(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
𝑥=5
2 𝑥 − 5 = 22
𝑥 − 5 = 10
𝑥+4-5=3
4 = 2𝑥 + 8
𝑥
5
= 2𝑥 − 9