Question

If y is equal to the square root of x, and x is doubled, how does that affect y?

Answer 1

If y is equal to the square root of x and x is doubled, then y will be equal to the square root of 2x

Explanation:

Let's say that y = sqrt(x). If x is doubled, then 2x = 2 * sqrt(x) * sqrt(x) = 2 * x Therefore, y = sqrt(2x)

Answer 2

when x is doubled, y will increase by
`\sf √(2)`

Explanation:

If y is equal to the square root of x, and x is doubled, it will affect y as follows:

Let's say
`\sf y = √(x)`

When x is doubled, it becomes 2x.

Now, let's find the new value of y, denoted as y'.

`\sf y' = √(2x)`

To understand how this affects y, let's compare y' with y.

`\sf y = √(x)` and
`\sf y' = √(2x)`

As you can see, y' involves the square root of 2x, while y involves the square root of x.

Since x is doubled in y', it means 2x is greater than x.

Hence, y' will be the square root of a larger number than y.

Mathematically:

`\boxed{\sf y' =√(2) y}`

In other words, doubling x increases the argument of the square root in y', leading to a larger value for y'.

Therefore, when x is doubled, y will increase in value.