Ximpledu

Radical

See how to solve a radical expression / equation / inequality.
32 examples and their solutions.

Square Root

Example

9
Solution

Example

-√25
Solution

Cube Root

Example

327
Solution

Example

3-8
Solution

Example

-3-1000
Solution

Simplifying a Radical

Example

4x2(x > 0)
Solution

Example

5a2bc6(a, b, c > 0)
Solution

Example

12x9(x > 0)
Solution

Adding and Subtracting Radicals

Example

3√2 + 2√5 + 5√2 - 8√5
Solution

Example

50 + √18 - √2
Solution

Multiplying Radicals

Example

6x × 3x3y(x, y > 0)
Solution

Example

(√3 + √2)(√6 - 2)
Solution

Dividing Radicals

Example

10xy32y(x, y > 0)
Solution

Rationalizing the Denominator

Example

7yx
Solution

Example

0.2
Solution

Example

14 + √3
Solution

Example

25 - √6
Solution

nth Root

Example

481
Solution

Example

5-32
Solution

Example

x2
Solution

Example

416x12y8
Solution

Rational Exponent

Formula

nam = amn

Example

316
Solution

Example

a79 = ?
Solution

Example

452
Solution

Example

3-72⋅ 352
Solution

Example

3x26xx
Solution

Radical Equation

Example

x + 6 = x
Solution

Radical Inequality

Example

2x - 3 < 5
Solution

Example

x > √x - 2 + 1
Solution

Square Root Function: Graph

Graph: y = √x

Graph of the Other Square Root Functions

Formula



y = a(x - h) + k

Example

y = √2x - 6 + 1
Domain?
Solution

Example

y = √-x + 4
Domain?
Solution

Example

y = -√x + 2
Domain?
Solution