Question

Solve your equation using trail and improvement. A number plus ten times its square root is is equal to one thousand

Answer 1

`x \approx 729`

Explanation:

Given

Let the number be x

So:

`x + 10\sqrt x = 1000`

Required

Using trial and improvement, find x

This implies that we keep guessing the values of x until we get a value that match the equation.

Let

`x = 625`

So, we have:

`x + 10\sqrt x = 1000`

`625 + 10 *√(625)`

Take the square root of 625

`625 + 10 *√(625) = 625 + 10 *25`

`625 + 10 *√(625) = 625 + 250`

`625 + 10 *√(625) = 875`

Let

`x = 729`

So, we have:

`x + 10\sqrt x = 1000`

`729 + 10 * √(729)`

Take the square root of 729

`729 + 10 * √(729) = 729 + 10 * 27`

`729 + 10 * √(729) = 729 + 270`

`729 + 10 * √(729) = 999`

At this point, we can conclude that x is approximately 729 because

`999 \approx 1000`

So:

`x \approx 729`