Master Radical Expressions: Conquer Radicals in Algebra I

Question 1

Identify which of the following numbers is irrational.

Accepted Answer

π

Answer

√(25)

Answer

√(9)

Answer

0.5

Question 2

Simplify the rational expression: (√(5) - √(2)) / (√(5) + √(2)).

Accepted Answer

√(5) + √(2)

Answer

√(5) - √(2)

Answer

5 - 2

Answer

5 + 2

Question 3

Multiply the radical expressions √2 and √8:

Accepted Answer

2√10

Answer

4

Answer

4√2

Question 4

Rationalize the denominator of the expression: 1 / √2

Accepted Answer

√2 / 2

Answer

2 / √2

Answer

√2 / 4

Question 5

Subtract the following radical expressions: **√(18x) - √(8x)**

Accepted Answer

√(10x)

Answer

√(18x - 8x)

Answer

2√(18x)

Answer

2√(10x)

Question 6

Rationalize the denominator of the following expression: **1/√(5)**

Accepted Answer

√(5)/5

Answer

√(5)

Answer

5/√(5)

Answer

5

Question 7

Which of the following numbers is **not** irrational?

Accepted Answer

√(9)

Answer

√(2)

Answer

π

Answer

5 + √2

Question 8

Multiply the radical expressions √12 and √3. What is the product?

Accepted Answer

6√3

Answer

6

Answer

2√36

Answer

36

Question 9

Identify the property of radicals that is not valid.

Accepted Answer

√(a + b) = √a + √b

Answer

√(a * b) = √a * √b

Answer

√(a/b) = √a/√b

Answer

√a^2 = a

Question 10

Simplify the radical expression: √12

Accepted Answer

2√3

Answer

3√4

Answer

4√3

Answer

6√2

Question 11

Which of the following is equivalent to √(-49)?

Accepted Answer

-7i

Answer

7i

Answer

49i

Answer

-49i

Question 12

Simplify the square root of 32.

Accepted Answer

4

Answer

2

Answer

8

Answer

16

Question 13

Multiply and simplify: √(2) * √(8).

Accepted Answer

4√(2)

Answer

2√(2)

Answer

4

Answer

8

Question 14

Subtract: √(18) - √(8).

Accepted Answer

2√(2)

Answer

√(10)

Answer

4√(2)

Answer

√(2)

Question 15

Rationalize the denominator: 1 / √(5).

Accepted Answer

√(5) / 5

Answer

5 / √(5)

Answer

5√(5)

Answer

√(5)

Question 16

Which of the following is NOT a property of radicals?

Accepted Answer

√(-a) = -√(a)

Answer

√(ab) = √(a) * √(b)

Answer

√(a / b) = √(a) / √(b)

Answer

√(a)^2 = a

Question 17

Simplify: (√(3) + √(2))^2.

Accepted Answer

5 + 2√(6)

Answer

5 - 2√(6)

Answer

11 + 2√(6)

Answer

11 - 2√(6)

Question 18

Simplify the expression: √18

Accepted Answer

3√2

Answer

6

Answer

2√3

Answer

9

Question 19

Multiply the expression: (2√5)(3√10)

Accepted Answer

6√50

Answer

6√2

Answer

10√50

Answer

5√50

Question 20

Simplify the expression: (√a + √b)^2

Accepted Answer

a + 2√ab + b

Answer

2√ab

Answer

a + b

Answer

a - b

Question 21

Which of the following is the discriminant of the quadratic equation: 2x^2 - 5x + 2 = 0?

Accepted Answer

25

Answer

5

Answer

1

Answer

-1

Question 22

Simplify the expression: (2√3 + 4)(2√3 - 4)

Accepted Answer

16 - 32√3

Answer

8 - 32√3

Answer

32 - 8√3

Answer

16 + 32√3

Question 23

Which step is NOT involved in adding radical expressions?

Accepted Answer

Multiply the radical sign by the entire other radical expression.

Answer

Simplify each radical expression as much as possible.

Answer

Combine like terms under the radical sign.

Answer

Leave the expression in radical form if possible.

Question 24

Multiply the radicals: √5 * √10.

Accepted Answer

√50

Answer

5√2

Answer

√15

Answer

10

Question 25

What is the expanded form of (√x - √y)²?

Accepted Answer

x - 2√(xy) + y

Answer

-2√(xy)

Answer

x + y

Answer

2√x + 2√y

Question 26

Simplify the expression: (√3 + √5)^2 - (√3 - √5)^2

Accepted Answer

32

Answer

16

Answer

64

Answer

128

Question 27

Which of the following expressions is irrational?

Accepted Answer

π/2

Answer

√2 + 3

Answer

0.5

Answer

5/4

Question 28

The area of a square is 64 cm^2. What is the length of one side of the square?

Accepted Answer

16 cm

Answer

8 cm

Answer

32 cm

Answer

64 cm

Question 29

Simplify the radical expression: √(125x^3y^2)

Accepted Answer

5x^2y

Answer

5x^3y

Answer

5x^4y^2

Answer

25x^3y^2

Question 30

Simplify the radical expression: (2x√3) + (5x√3)

Accepted Answer

7x√3

Answer

2x√9

Answer

x√15

Answer

5x√6

Question 31

Subtract the radical expressions: (4√5) - (2√5)

Accepted Answer

2√5

Answer

6√5

Answer

2√10

Answer

4

Question 32

Which of the following is NOT a property of radicals?

Accepted Answer

√(a + b) = √a + √b

Answer

√(ab) = √a√b

Answer

√(a^n) = a^(n/2)

Answer

(√a)^n = √(a^n)

Question 33

Determine the relationship between the values of √(125) and 5√5. Provide a clear explanation to justify your answer.

Accepted Answer

√(125) is equal to 5√5 because 125 can be expressed as 25(5).

Answer

√(125) is greater than 5√5 because 125 is greater than 25.

Answer

√(125) is less than 5√5 because 125 is less than 100.

Answer

√(125) is an irrational number, whereas 5√5 is a rational number.

Question 34

Divide the expressions: (4√2) ÷ (√8)

Accepted Answer

2√2

Answer

√2

Answer

4√8

Answer

16

Question 35

Add the expressions: (2√3) + (5√3)

Accepted Answer

7√3

Answer

7√6

Answer

3√6

Answer

10√3

Question 36

Simplify the expression: √(a^2 - b^2)

Accepted Answer

a - b

Answer

a + b

Answer

a√(1 - b)

Answer

a√(1 + b)

Question 37

Which of the following expressions simplifies to 3?

Accepted Answer

√25 - √16

Answer

√25 + √16

Answer

√16 - √25

Answer

√16 + √25

Question 38

Simplify the expression: (2x²y√3)³

Accepted Answer

16x⁶y³√27

Answer

16x⁶y³√3

Answer

8x⁶y³√3

Answer

8x⁶y³√27

Question 39

Solve the equation: |2x - 5| = 7

Accepted Answer

x = 6 or x = 1

Answer

x = 3 or x = 4

Answer

x = -3 or x = 4

Answer

x = 6

Question 40

Determine the degree of the expression ∛(x³y²z).

Accepted Answer

6

Answer

3

Answer

2

Answer

4

Question 41

Solve for x: √(x + 5) = 4

Accepted Answer

x = 11

Answer

x = 9

Answer

x = -9

Answer

x = -11

Question 42

Solve for y: √(y² - 4) = 2

Accepted Answer

y = ±2√2

Answer

y = ±2

Answer

y = 2√2

Answer

y = -2√2

Question 43

Add the radicals: 5√2 + 3√2.

Accepted Answer

8√2

Answer

2√2

Answer

-2√2

Answer

15√2

Question 44

Solve for x: x^2 = 12. Express your answer in simplified radical form.

Accepted Answer

±2√3

Answer

±4

Answer

±6

Question 45

Rationalize the denominator of the expression: √(6) / √(3)

Accepted Answer

3√(6) / 3

Answer

3√(6) / 9

Answer

6 / √(3)

Answer

18 / 3

Question 46

Simplify the radical expression:
√(80x³y⁴)

Accepted Answer

4x√5y²

Answer

40x²y³

Answer

8x√5y²

Answer

16x²y²

Question 47

Simplify the radical expression: √(12)

Accepted Answer

2√3

Answer

√6

Answer

6

Answer

3√4

Question 48

Rationalize the denominator of the expression: 1 / √(5)

Accepted Answer

√(5) / 5

Answer

5

Answer

√(5)

Answer

5 / √(5)

Question 49

Simplify the expression: (√(x) + √(y))²

Accepted Answer

x + y + 2√(xy)

Answer

xy

Answer

x + y

Question 50

Which of the following is NOT a property of radicals?

Accepted Answer

Radicals can be distributed over addition and subtraction.

Answer

The product of two radicals is a radical.

Answer

The quotient of two radicals is a radical.