# The product of a positive number, its square, and its reciprocal is 100/81. What is the number?

Oct 31, 2016

The 10 divided by 9

#### Explanation:

The equation for this problem would be

$x \times {x}^{2} \times \frac{1}{x} = \frac{100}{81}$ This reduces to

${x}^{2} = \frac{100}{81}$ Take the square root of both sides gives

$x = \frac{10}{9}$

Oct 31, 2016

color(blue)(n=10/9

#### Explanation:

I'd like to answer this question (but was asked by me and then I found the answer)

Let the number be $n$

Then,

color(orange)("Its reciprocal"=1/n

color(orange)("Its square"=n^2

Let's put everything according to the question

$\rightarrow n \times {n}^{2} \times \frac{1}{n} = \frac{100}{81}$

$\rightarrow \cancel{n} \times {n}^{2} \times \frac{1}{\cancel{n}} = \frac{100}{81}$

$\rightarrow {n}^{2} = \frac{100}{81}$

Take the square root of both sides

$\rightarrow \sqrt{{n}^{2}} = \sqrt{\frac{100}{81}}$

$\rightarrow n = \frac{\sqrt{100}}{\sqrt{81}}$

color(blue)(rArrn=10/9