Square roots and Cube 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
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
Example: Simplify: – + 4
7 × 7 × 7 = 343, so = 7
14 × 14 = 196, so = 14
so , – + 4 = 7 – 14 + 4 = 11 -14 = -3
- 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?
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The Number System
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