# Simplify each of this following surd

1. Aug 8, 2015

### jonathan22

1. The problem statement, all variables and given/known data
3∜2 - ∜(2/81) + ∜32 - ∜162

2. Relevant equations

3. 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??

2. Aug 8, 2015

### Staff: Mentor

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?

3. Aug 8, 2015

### jonathan22

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

4. Aug 8, 2015

### Staff: Mentor

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.

5. Aug 8, 2015

### jonathan22

ok, but how to solve ∜(2/81)?

6. Aug 8, 2015

### Staff: Mentor

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

7. Aug 8, 2015

### HallsofIvy

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