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
Personalized Online Tutoring from eTutorWorld
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 TRIAL Session.
No credit card required, no obligation to purchase.
Just schedule a FREE Sessions to meet a tutor and get help on any topic you want!
Learn more about Scientific Method and other important topics with 7th Grade Science Tutoring at eTutorWorld. Our expert science tutors break down the topics through interactive one-to-one sessions. We also offer the advantage of customized lesson plans, flexible schedules and convenience of learning from home.
Pricing for Online Tutoring
| Tutoring Package | Validity | Grade (1-12), College |
|---|---|---|
| 5 sessions | 1 Month | $124 |
| 1 session | 1 Month | $25 |
| 10 sessions | 3 months | $239 |
| 15 sessions | 3 months | $354 |
| 20 sessions | 4 months | $449 |
| 50 sessions | 6 months | $1049 |
| 100 sessions | 12 months | $2049 |
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
