Algebra 1 - Radical Expressions Overview

Simplify the following expression. 7 - √2 / 1 + √2

-9 + 8√2

Solve the following equation: √(2x) = 1.

0.5

Simplify. √16/√4

2

Simplify. 4/∛27

4/3

Which mnemonic can help when multiplying two binomials?

FOIL

Simplify. √30xy

It can not be simplified further.

Simplify 3√3 - 2√2

It can not be simplified.

Which of these are examples of real numbers? i. any number that is not imaginary. ii. numbers that do not include ∞ and √(-1) iii. examples include -3, 2.71, 4/5, and √2

i, ii and iii

Simplify the following expression. √15xy^2 / √5xy

√3y

Simplify ∛(5/8)

∛5 / 2

Which shows the correct factorization for 2304? a. (2*2)*(2*2)*(2*2)*(3*3)*3 b. (2*2)*(2*2)*(2*2)*(2*2)*(3*3)*2 c. (2*2)*(2*2)*(3*3)*2 d. (2*2)*64 e. (2*2)*(2*2)*(2*2)*(2*2)*(3*3)

e. (2*2)*(2*2)*(2*2)*(2*2)*(3*3)

Which number is an imperfect square? a. 1 b. 400 c. 16 d. 144 e. 415

e. 415

Which of these terms is possible to add to √5? a. 26√5 b. -15√5 c. -2√5 d. 4√5 e. All of them could be added to radical 5

e. All of them could be added to radical 5

In mathematics, the term 'radical' means the same as

square root

Simplify √x^2 =

x

Simplify √x^3 y^5 z

xy^2 √xyz

Simplify √3 (x + √5)

x√3 + √15

Simplify the following expression. √3x^2 y^3 / √5x^3 y^2

√15xy/5x

Simplify the following expression. (Make sure to simplify it completely.) 4/√8

√2

What is the smallest term that could be multiplied to this term to create a perfect square? √27

√3

Solve the following equation: √(x + 6) = √(3x + 4)

1

Solve: √2

1.414

Simplify. 1/√25

1/5

Simplify √200

10√2

Solve: √121

11

Simplify (4 + √2x) (3 - √x)

12 - 4√x + 3√2x - x√2

Simplify the following expression. 3 / 5 + √2

15 - 3√2 / 23

Solve the following equation: √(x-2) = 4.

18

Solve the following equation: ∛x = 6

216

Simplify: √1152

24√2

Solve: √625

25

Simplify 2√x (√x - √2)

2x - 2√2x

Simplify (x - √2)(2x + √8)

2x^2 - 4

Simplify the following expression. 4 / √18

2√2 / 3

Multiply the following expressions: ∛20 * ∛10

2∛25

Simplify. ∛24

2∛3

Solve the following equation. √(3x + 7) + 2 = √(7x + 15)

3

Solve the following equation. √(5x - 9) = √(2x)

3

What number is left inside the radical after you simplify? √48

3

What number is left inside the radical after you simplify? ∛192

3

What number is on the outside after simplifying? ∛54

3

Which expression is the conjugate of the following? 3 + √7

3 - √7

Which of the following is NOT a factor of 72? √72 a. 4 and 18 b. 36 and 2 c. 3 and 14 d. 12 and 6 e. 9 and 8

3 and 14

Simplify √45a^2

3a√5

Simplify √18x^3 y^5 / √2xy

3xy^2

Which of the following terms is written in proper form? a. 5√(7/10) b. √x^3 / √x c. 3√5 / 5 d. 1 / c-√7 e. They are all written in the correct form.

3√5 / 5

Simplify √80x^3 y^2

4xy √5x

Simplify √50 / √2

5

Simplify. √50ab

5√2ab

Simplify: √175

5√7

Simplify the following expression. (Hint: How can you get a perfect cube in the denominator?) 10/∛2

5∛4

After you simplify this radical, what number is on the outside of the radical? √72

6

Solve the following equation: 2 + √c = 27.

625

Simplify. √108x^3 y^4

6xy^2 √3x

Simplify 5√2x - 2√2 + √2x - 3√2

6√2x - 5√2

Simplify 6√x + √x

7√x

Solve: √64

8

Simplify: √192

8√3

Solve the following equation: √x = 3.

9

Solve: √81

9

Which one of the following statements is NOT true about the quotient rule?

All of the statements are true.

Solve the following equation. √(3 - x) = √(2 + x) + 1

-1

Simplify √7 + 4√2 - √2 + 2√2 - 9√7 + 3√7

-5√7 + 5√2

Multiply the following expressions. ∛2xy^2 * √5x^3 y^2

The indices are different so the terms cannot be multiplied and simplified without using advanced mathematical techniques

Which of the following is NOT a step when solving radical equations with two radical terms?

These are all steps to solving radical equations with two radicals.

How are squared and square root related?

They are inverse operations.

Simplify. √a^5 b^2 c

a^2 b√ac

Multiply, then simplify the following expressions: √ab^3 * √a^2 b^4

ab^3 √ab

Simplify (Make sure your answer is fully simplified.) √6a^2 / √75b

a√2b / 5b

Which of the following needs to be simplified further? a. 25/26 b. 25/√6 c. 3/2 d. 25/4 e. 1/4

b. 25/√6

Which of the following are not real numbers? a. 17 b. ∞ c. 5 d. all of them are real numbers e. none of them are real numbers

b. ∞

Which of the following statements is true about multiplying and simplifying radical expressions? a. The expressions cannot equal zero. b. It is not necessary to simplify after multiplying. c. It can be done if the index of each radical is the same. d. All of the answers are correct.

c. It can be done if the index of each radical is the same.

Which of the following demonstrates the product rule for radicals when multiplying radical expressions? a. √x * ∛y = (5)√xy b. ∛x * √x = (4)√x c. √3 * √4 = √3*4 d. √3 * √4 = 2√3

c. √3 * √4 = √3*4

Which of the following terms is the radicand for the following expression? (2)√23a^5 bc^2 a. a^5 bc^2 b. 23 c. a^5 d. 23a^5 bc^2 e. 2

d. 23a^5 bc^2

Which term is the radicand in this expression? 5 ∛x^2 a. 3 b. 5 c. 5 ∛x^2 d. x^2 e. There is no radicand Print Worksheet

d. x^2

Which of the following represents a real number? a. √∞ b. √-1 c. √-4 d. √2.68 e. They are all real numbers.

d. √2.68