SIMPLIFY RADICAL EXPRESSIONS

If n is even number, then n^th root of the negative number is not real.

• If we have square root, for every two values or variables inside the square we can take one out of it.
• If we have cube root, for every three values or variables inside the cube root, we can take one out of it.
• If we have fourth root, for every four values or variables inside the fourth root, we can take one out of it.

Simplify the radical expression using the definition.

Example 1 :

√(4(y - 1)²)

Solution :

= 2|y - 1|

Example 2 :

∛(-8x³y⁶)

Solution :

Example 3 :

5^th root (2x - 1)⁵

Solution :

Example 4 :

∜(16x⁸)

Solution :

Example 5 :

∛(-27x³)

Solution :

Example 6 :

∜(16a¹²y²)

Solution :

Example 7 :

√x / ∛x

Solution :

Example 8 :

√(∛x)

Solution :

Example 9 :

√(x+7)√(x-7)

Solution :

= √(x+7)√(x-7)

= √(x+7)(x-7)

Here (x+7)(x-7) looks like (a + b) (a - b) = a² - b²

= √(x+7)(x-7)

= √(x² - 7²)

Example 10 :

√50

Solution :

= √50

Decomposing 50 into prime factors, we get

= √(5⋅5⋅2)

= 5√2