Question

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

Answer 1

Answer:

$x \approx 729$

Step-by-step 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:

$x + 10\sqrt x = 1000$

$625 + 10 *\sqrt{625}$

Take the square root of 625

$625 + 10 *\sqrt{625} = 625 + 10 *25$

$625 + 10 *\sqrt{625} = 625 + 250$

$625 + 10 *\sqrt{625} = 875$

Let

$x = 729$

So, we have:

$x + 10\sqrt x = 1000$

$729 + 10 * \sqrt{729}$

Take the square root of 729

$729 + 10 * \sqrt{729} = 729 + 10 * 27$

$729 + 10 * \sqrt{729} = 729 + 270$

$729 + 10 * \sqrt{729} = 999$

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

$999 \approx 1000$

So:

$x \approx 729$