323334RadicalExpressions

Question 1

What is a radical expression?

Answer 1

any equation which contains a radical

Question 2

What is a radical?

Answer 2

An expression which expresses the root of a number.
√5
third root of√8

Question 3

How do you simplify radicals?

Answer 3

Look for roots within the radical:

√162 = √(81*2) = 9√2

Question 4

Simplify:

√(80x⁷)

Answer 4

√(80x⁷)

√(16*5*x⁶*x)

= 4x³√(5x)

(x³)² = x⁶

Question 5

Which is easier with radicals:

addition/subtraction or

multiplication/division ?

Answer 5

multiplication/division

Question 6

Simplify:

√(98x⁵) * √(18x³)

Answer 6

= √(2*49*x⁴*x)*√(9*2*x²*x)

= 7x²√2x) * 3x√2x

=21x³*2x

= 42x⁴

Question 7

Simplify:

√(75t⁹/12t³)

Answer 7

√(75t⁹/12t³)

√(75t⁹)/√(12t³)

= √(25*3*t⁸*t)/√(4*3*t²*t)

= 5t⁴√3t / 2t√3t

= ^5t³/₂

Question 8

Simplify:

^5√2/_√(25x)

Answer 8

^5√2/_√(25x)

^5√2/_5√(x)

=^√2/_√x

Question 9

What is rationalizing the denominator?

Answer 9

Taking the radical out fo the denominator.

Question 10

Rationalize

^√2/_√x

Answer 10

Multiply by ^√x/_√x

= √(2x)/x

Question 11

How do you add and subtract radicals if the radicals are the same?

Answer 11

Just add:

3√2 + 5√2 = 8√2

[Just as 3*2 + 4*2 = 7*2]

Question 12

What if the radicals are not the same?

Answer 12

Try to make them the same.

Question 13

Solve:

11√3 - √12

Answer 13

11√3 - √12

= 11√3 - 2√3

= 9√3

Question 14

Solve:

13√5 - 3√125 + √100

Answer 14

13√5 - 3√125 + √100

= 13√5 - 15√5 + 10

= 10 - 2√5

Question 15

Simplify:

√3 + √5

Answer 15

It can’t be simplified.

Question 16

Solve:

√3 * (5√3 + 7)

Answer 16

Use distribution:

= 15 + 7√3

Question 17

What are conjugates?

Answer 17

A conjugate is created when you change the sign in the middle of a binomial.

Question 18

Solve:

(√3 + √11)(√3 - √11)

Answer 18

(√3 + √11)(√3 - √11)

= 3 - 11 = -8

Question 19

What is another term for conjugates?

Answer 19

A difference of 2 squares

Question 20

What is (√x)²?

Answer 20

(√x)²

If x > 0, it is x

Question 21

Solve:

√x - 7 = 2

Answer 21

√x - 7 = 2

√x = 9

x = 9²

Question 22

Solve:

√(t - 2) = 5

Answer 22

√(t - 2) = 5

t - 2 = 25

t = 27

Question 23

Solve:

√(x + 3) = √(5x - 9)

Answer 23

√(x + 3) = √(5x - 9)

x + 3 = 5x - 9

x = 3

Question 24

Solve:

3x = 2x + √(4x + 5)

Answer 24

3x = 2x + √(4x + 5)

x = √(4x + 5)

x² = 4x + 5

Quadratic equation:

x² - 4x - 5 = 0

(x - 5)(x + 1)

x = 5 or -1

^{Check. -1 is an extraneous solution}

Question 25

Solve:

8 + √(4y) = 4

Answer 25

8 + √(4y) = 4

√(4y) = -4

No solution.

The square root of 16 is not -4

Question 26

Solve:

√(2x² + 8x - 33) = x

Answer 26

√(2x² + 8x - 33) = x

2x² + 8x - 33 = x²

x² + 8x - 33 = 0

(x + 11)(x - 3) = 0

x = 3 and -11

-11 does not work

Question 27

What is the domain of √x?

Answer 27

Positive numbers

Question 28

What is the domain of √(x - 3)?

Answer 28

All positive numbers ≥ 3

Question 29

Compare the graphs of

y = √x and

y = √(x - 3)

Answer 29

y = √(x - 3) is the graph of

y = √x moved 3 to the right.

Question 30

How does the graph of

y = √x + 4 compare to

the graph of √x?

Answer 30

It is moved up the y-axis 4.