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

`x = 5`

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`