## Algebra 1 radicals

**Introduction :**

Algebra is one of the most basic element of mathematics in which, we switch from basic arithmetic to variables. Algebra covers a large number of subdivisions like polynomials, rational, exponents, logarithms, expressions etc under it. Algebra 1 covers few topics from them. Radicals come under algebra 1. Radicals are terms in mathematics which has a root on them. The radical may be a square root , cube root, etc. In algebra 1 basic operation like multiplication, division on radicals is done. The properties of radicals and examples on them are given in the following sections.

Properties of radicals:

1. The product of two square roots with different numbers inside can be written in a single root with the product of those two numbers.

2. When a number gets into the square root, it turns into a square of the number.

3. The square root of a fraction can be written as individual roots.

4. When a perfect square comes out of the root, it becomes the number without square.

**Let’s make it clear with some examples:**

1. √x × √y =√ (xy) [According to the first property]

2. x √y = √x^2y [According to the second property]

3. √(x/y) = √x/√y [According to the third property]

4. √yx2 =x √y. [According to the fourth property]

5. `root(n)(x)` = 2 ===> x = `2^(1/n)`

6. `sqrtx` = x1/2

7. `root(3)(x)` = x1/3

Examples on algebra 1 radicals:

**Example 1:**

**Algebra Example 1:**

Simplify the expression`(root(3)(2^3))^4`

**Solution:**

The given expression is `(root(3)(2^3))^4`

It can be represented as (`(2^3)^(1/3)` )4

Therefore, (`2^(3/3)` )4

= 24

= 2*2*2*2 = 16

Therefore, The simplified answer for the expression is 16.

**Algebra Example 2:**

Simplify the expression`(root(2)(2^3))^4`

**Solution:**

The given expression is `(root(2)(2^3))^4`

It can be represented as (`(2^3)^(1/2)` )4

Therefore, (`2^(3/2)` )4

= `2^(12/2)`

= 26 = 2*2*2*2*2*2 = 64

Therefore, The simplified answer for the expression is 64.

**Algebra Example 3:**

Simplify the expression`(root(2)(2^3))^2`

**Solution:**

The given expression is `(root(2)(2^3))^2`

It can be represented as (`(2^3)^(1/2)` )2

Therefore, (`2^(3/2)` )2

= `2^(6/2)`

= 23 = 2*2*2 = 8

Therefore, The simplified answer for the expression is 8.

Practice problems on rational exponents:

Here are few practice problems given to make sure that the students have learned the above mentioned Rational Exponents Solver concept,

1. Simplify the expression `root(5)(x)` = 2 , and find the value of 'x'

2. Simplify the expression `root(3)(27)`

Solution:

`1. x =32`

`2. 3`