Question 740065

let a non zero number be {{{x}}}
{{{30}}} times the square root of a non zero number is {{{30sqrt(x)}}}

equal to {{{8}}} times the number is {{{8x}}}

so, we have

{{{30sqrt(x)=8x}}}...you can solve for {{{x}}} if you square both sides

{{{(30sqrt(x))^2=(8x)^2}}}

{{{30^2(x)=64x^2}}}

{{{900x=64x^2}}}

{{{64x^2-900x=0}}}

{{{x(64x-900)=0}}}....use zero product rule

{{{x(64x-900)=0}}} if {{{x=0}}}..this is a solution, but our number should be non zero; so, we need other solution

or if {{{(64x-900)=0}}} => {{{64x=900}}}=> {{{x=900/64}}}=> {{{x=14.0625}}}

so, a non zero number be {{{x=14.0625}}} and this is your solution

let's check this solution:

{{{30sqrt(x)=8x}}}

{{{30sqrt(14.0625)=8*14.0625}}}

{{{30(3.75)=112.5}}}

{{{112.5=112.5}}}.....this confirms that our answer is correct