# Square roots and Cube roots

## Square Roots

The square root of a positive number ‘*n*’ is that number which, when multiplied by itself, gives ‘*n*’.

There are two square roots for a positive number. For example, the square roots of 25 are +5 and -5. The positive square root of a number is called the principal square root.

The symbol √ is called the radical sign. The index notation is also used instead of the radical sign. For example:

= +4 can be written as = +4 .

*Example:* Find the square root of 81.

81 = 9 × 9

= 9

## Cube Roots

The cube root of a positive number ‘*N*’ is that number which, when multiplied by itself twice, gives ‘*N*’.

For example, the cube root of 8 is 2 because 2 × 2 × 2 = 8 (here 2 is being multiplied by itself twice)

The symbol for cube root is a radical sign with a small 3 on the left ∛ .

*Example:* Find the cube root of -125.

-125 = (-5)^{3} = -5 × -5 × -5

= **-5**

*Example: *Simplify: – + 4

7 × 7 × 7 = 343, so = 7

14 × 14 = 196, so = 14

so , – + 4 = 7 – 14 + 4 = 11 -14 = **-3**

### CHECK POINT

- Find the square root of 169.
- What is the cube root of 1331?
- Simplify: + – 5
- Value of –
- What is the square root of 1,024?

##### Answer key

- 13
- 11
- 1
- 12
- 32

## eTutorWorld Understands Math Tutoring | Online Math Worksheets are Important Tools

Understanding graphs, charts, and opinion polls in a newspaper, for calculating house and car payments, and for choosing a long-distance telephone service are impossible without strong math skills …and the only way to develop strong math skills is by constant practice.

‘Practice makes a man perfect’ holds true for no other field better than for math. A middle or high school student must set aside a minimum of an hour for math every day. Other than textbooks, worksheets help you revise and understand concepts better.

Our expert tutors prepare online maths worksheets that are age and grade-appropriate. Grade-wise math worksheets for Elementary Math, Arithmetic, Pre-Algebra, Algebra, Geometry, Trigonometry, Statistics, Pre-Calculus and Calculus can be solved to improve math skills, to get ahead or to even catch up.

You may download these FREE online math worksheets in the PDF format, and then print and email us their solutions for a free evaluation and analysis by eTutorworld’smath expert tutors.

You may solve these worksheets by yourself or with your peers while studying together.

The Answer Key at the end of each worksheet allows for a self-evaluation.

## Personalized Online Tutoring

eTutorWorld offers affordable one-on-one live tutoring over the web for Grades K-12, Test Prep help for Standardized tests like SCAT, CogAT, MAP, SSAT, SAT, ACT, ISEE and AP. You may schedule online tutoring lessons at your personal scheduled times, all with a Money-Back Guarantee. The first one-on-one online tutoring lesson is always FREE, no purchase obligation, no credit card required.

For answers/solutions to any question or to learn concepts, take a **FREE CLASS.**

*No credit card required, no obligation to purchase. **Just book a free class to meet a tutor and get help on any topic you want!*

## Pricing for Online Tutoring

Tutoring Package | Validity | Grade (1-12), College |
---|---|---|

5 sessions | 1 Month | $139 |

1 session | 1 Month | $28 |

10 sessions | 3 months | $269 |

15 sessions | 3 months | $399 |

20 sessions | 4 months | $499 |

50 sessions | 6 months | $1189 |

100 sessions | 12 months | $2249 |

__Arithemetic & Pre Algebra__

**The Number System**

1) Rational and Irrational Numbers

2) Compare Irrational Numbers

3) Fractions and Repeating Decimals

4) Approximating Square Roots

__Algebra__

**Expressions and Equations**

1) Exponents and their properties

2) Square roots and Cube roots

3) Scientific Notation – addition, subtraction, division and multiplication

4) Equations with variables on both sides

5) Linear equations with one, zero, or infinite solutions

6) Age Word Problems

7) Solve systems of linear equations with elimination and substitution

8) Word Problems on System of Linear Equations

__Geometry__

1) Parallel Lines

2) Congruent Angles

3) Finding Angle Measures

4) Pythagorean Theorem

5) Distance Formula

6) Word problems on Volume of Cones, Cylinders, and Spheres

__Statistics and Probability__

## IN THE NEWS

Our mission is to provide high quality online tutoring services, using state of the art Internet technology, to school students worldwide.

**Online test prep and practice**

SCAT

CogAT

SSAT

ISEE

PSAT

SAT

ACT

AP Exam

**Science Tutoring**

Physics Tutoring

Chemistry Tutoring

Biology Tutoring

**Math Tutoring**

Pre-Algebra Tutoring

Algebra Tutoring

Pre Calculus Tutoring

Calculus Tutoring

Geometry Tutoring

Trigonometry Tutoring

Statistics Tutoring

**Quick links**

Free Worksheets

Fact sheet

Sales Partner Opportunities

Parents

Passive Fundraising

Virtual Fundraising

Our Expert Tutors

Safe and Secure Tutoring

Interactive Online Tutoring

After School Tutoring

Elementary School Tutoring

Middle School Tutoring

High School Tutoring

Home Work Help

Math Tutors New York City

Press

©2022 eTutorWorld Terms of use Privacy Policy Site by Little Red Bird

©2022 eTutorWorld

Terms of use

Privacy Policy

Site by Little Red Bird