+0

+1
427
4
+1466

Exercise: Perform the operation indicated

3√16 x 73 √2

Feb 16, 2018

#1
+9180
+2

$$\quad\sqrt[3]{16}\,\times\,7\sqrt[3]{2} \\ =\\ \quad \sqrt[3]{16}\,\times\,7\,\times\,\sqrt[3]{2} \\ =\\ \quad \sqrt[3]{16}\,\times\,\sqrt[3]{2}\,\times\,7 \\ =\\ \quad \sqrt[3]{16\,\times\,2}\,\times\,7 \\ =\\ \quad \sqrt[3]{2\,\times\,2\,\times\,2\,\times2\,\times\,2}\,\times\,7 \\ =\\ \quad \sqrt[3]{2^3\,\times\,2^2}\,\times\,7 \\ =\\ \quad \sqrt[3]{2^3}\,\times\,\sqrt[3]{2^2}\,\times\,7 \\ =\\ \quad 2\,\times\,\sqrt[3]{4}\,\times\,7 \\ =\\ \quad 2\,\times\,7\,\times\,\sqrt[3]{4} \\ =\\ \quad 14\,\times\,\sqrt[3]{4} \\ =\\ \quad 14\sqrt[3]{4} \\$$

.
Feb 16, 2018
#2
+1466
+1

Thanks Hectitar but I think the correct answer is

686 x 25/6

I checked it with Wolfram Alpha

(http://www.wolframalpha.com/input/?i=%5E3%E2%88%9A16+x+7%5E3%E2%88%9A2)

Plus I checked it with another calculator and the answer was: 686 x 25/6

Feb 16, 2018
#3
+114140
+3

Just a  slight mis-interpretation......no big deal

So we have

3√16 * 73 √2   =

3√16  * 343√2  =

3√8  * 3√2  *  343√2  =

2 * 3√2  *  343√2  =

2 * 343  *  (2)1/3  * (2)1/2   =

686 * (2)2/6 * (2)3/6   =

686 * (2)5/6

Feb 16, 2018
#4
+1466
+1

Thank You All!!

Feb 16, 2018