## Radicals – about radicals – pg.1/7

**Radicals: pg. 1, 2, 3, 4, 5, 6, 7**

**Radicals: pg. 1, 2, 3, 4, 5, 6, 7**

**Contents:**

**Contents:**

*pg.1…..Radicals – about radicals*

*pg.1…..Radicals – about radicals*

*pg.2…..Radicals – properties (addition, subtraction, multiplication, division)*

*pg.2…..Radicals – properties (addition, subtraction, multiplication, division)*

*pg.3…..Radicals – properties (raising to the power)*

*pg.3…..Radicals – properties (raising to the power)*

*pg.4…..Radicals – properties (radicals conditions to exist in the real numbers world)*

*pg.4…..Radicals – properties (radicals conditions to exist in the real numbers world)*

*pg.5…..Radicals – **hand calculation of square root*

*pg.5…..Radicals –*

*hand calculation of square root*

*pg.6…..Radicals – **exercises*

*pg.6…..Radicals –*

*exercises*

*pg.7…..Radicals – answers to **exercises*

*pg.7…..Radicals – answers to*

*exercises*

*About radicals*

*About radicals*

**A radical is written as where ***n* is called *index *and is always equal or larger than *2 ***( ), is called ***radical sign* and *m* is called *radicand*** ( is read: ***n*th root of *m*).

*n*is called

*index*and is always equal or larger than

*2*

*radical sign*and

*m*is called

*radicand*

*n*th root of

*m*).

**To find the ***n*th root of a number, we need to find the number that raised to the power *n* is equal with that number (radicand).

*n*th root of a number, we need to find the number that raised to the power

*n*is equal with that number (radicand).

### Radicals are exponential expressions that have as exponent a fraction.

### A radical can be written as an exponential expression:

**[1]**

**If , by using the expression [13] from ***Exponential Expressions Presentation*, [1] becomes:

*Exponential Expressions Presentation*, [1] becomes:

**The general formula for a radical can be written:**

### [2] where

**Example: **

**Example:**

** When the radicand is ***0* the radical is equal with *0* no matter what value the index has.

*0*the radical is equal with

*0*no matter what value the index has.

### [3]

**Example:**

**Example:**

* *When the index has the value *2*, the radical is read *square root of* *m*.

*When the index has the value*

*2*, the radical is read

*square root of*

*m*.

**Note that, when the index is 2, we write the radical without the index.**

**Note that, when the index is 2, we write the radical without the index.**

*Example:* is read square root of .

*Example:*

* *When the index of a radical has the value *3*, the radical is read *cube root of* *m*.

*When the index of a radical has the value*

*3*, the radical is read

*cube root of*

*m*.

*Example:* is read cube root of *4*.

*Example:*is read cube root of

*4*.

**Radicals: pg. 1, 2, 3, 4, 5, 6, 7**

**Radicals: pg. 1, 2, 3, 4, 5, 6, 7**

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