Simplify each of this following surd

[jonathan22]

Homework Statement

3∜2 - ∜(2/81) + ∜32 - ∜162

Homework Equations

The Attempt at a Solution

3∜2 - ∜(2/81) - ∜130
3∜2 – ∜2/3 - ∜130
exactly when i tried to calculate, i got problem with the next of this calculating, i confused. Can anybody help me for do the next of this calculating??[/B]

 

[mfb]

Where does the 130 come from? That looks like an incorrect transformation.

Did you split the numbers in the square roots into their prime factors?

 

[jonathan22]

oh i wrong, i mean 3∜2 - ∜(2/81) - ∜130
3∜2 – ∜2/3 - ∜130, and then the 130 come from 32-162

 

[Mark44]

Homework Statement

3∜2 - ∜(2/81) + ∜32 - ∜162

oh i wrong, i mean 3∜2 - ∜(2/81) - ∜130
3∜2 – ∜2/3 - ∜130, and then the 130 come from 32-162

First off, 32 - 162 = -130. More importantly, $\sqrt[4]{a} - \sqrt[4]{b} \ne \sqrt[4]{a - b}$.
As already mentioned simpligy $\sqrt[4]{162}$ by factoring 162 into its prime factors.

 

[jonathan22]

ok, but how to solve ∜(2/81)?

 

[mfb]

That part was right. $$ \frac{\sqrt[4]2}{3}$$

 

[HallsofIvy]

It helps to know that 81= 3^4 and 162= 2(3^4).