# 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

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__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__