Question

An expression is given that has a value between 4.44.4 and 4.54.5, and where xx represents an integer. ​ ​ \sqrt{x}+\sqrt{x} x ​ + x ​ ​ What is the value of xx?

Answer 1

Answer:

$x = 5$

Step-by-step explanation:

Given

$\sqrt x + \sqrt x = (4.4,4.5)$

Required

Find x

When the result is 4.4, we have:

$\sqrt x + \sqrt x = 4.4$

This gives:

$2\sqrt x = 4.4$

Divide both sides by 2

$\sqrt x = 2.2$

Square both sides

$x = 2.2^2$

$x = 4.84$

When the result is 4.5, we have:

$\sqrt x + \sqrt x = 4.5$

$2\sqrt x = 4.5$

Divide both sides by 2

$\sqrt x = 2.25$

Square both sides

$x = 2.25^2$

$x = 5.0625$

So, the value of x is between 4.84 and 5.0625

i.e.

$x = (4.84,5.0625)$

The only integer between the above interval is 5.

Hence:

$x = 5$