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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