I am trying to solve a problem for algebr and keep getting a different answer then my text book. The problem involves cube roots. I am wondering how I am getting this wrong and how to solve it.
$\endgroup$ 8Problem : $$\sqrt[3]{\frac{16}{54}}$$
My answer : $$\frac{2 \sqrt[3] 2}{ 3\sqrt[3] 2}$$
Book : $$\sqrt[2]{\frac{8}{27}}$$
2 Answers
$\begingroup$Both are one and the same thing!
You're Right!
$\dfrac{2 \sqrt[3] (2)}{ 3\sqrt[3] (2)}$=$\dfrac 23 $=$\sqrt[3]{8/27}$
$2^3=8,3^3=27$
$\endgroup$ 4 $\begingroup$There must be a typo...in the book's solutions, if they show $\sqrt[\Large 2]{\dfrac 8{27}}$ That happens all too frequently.
You are correct, save for the fact that you could have simplified by canceling the common term in the numerator and the denominator, as I did to move from the second to the final equality.
$$\left(\dfrac{16}{54}\right)^{1/3} = \left(\dfrac{2\cdot 8}{2\cdot 27}\right)^{1/3}= \sqrt[\Large 3]{\dfrac{8}{27}} = \dfrac 23$$
$\endgroup$ 2
