## How do you find the range of a root?

To draw the graph of the f(x)=√x−2, shift the graph of y=√x two units to the right. Range = [0,∞)= {y: y≥0}. We can find the domain of this function algebraically by examining its defining equation f(x)=√x−2. We understand that we cannot take the square root of a negative number.

**What is the range of the square root function?**

[ 0 , ∞ [

The range of a function is the set of all possible function values. We know that the range of the square root function √ 𝑥 is [ 0 , ∞ [ . In other words, for any number 𝑦 in the interval [ 0 , ∞ [ , we can find some number 𝑥 that satisfies 𝑦 = √ 𝑥 .

**Why is √ 2 an irrational number?**

The actual value of √2 is undetermined. The decimal expansion of √2 is infinite because it is non-terminating and non-repeating. Any number that has a non-terminating and non-repeating decimal expansion is always an irrational number. So, √2 is an irrational number.

### Is root 2 a rational number?

Sal proves that the square root of 2 is an irrational number, i.e. it cannot be given as the ratio of two integers.

**What is the range in maths?**

The range is the difference between the highest and lowest values in a set of numbers. To find it, subtract the lowest number in the distribution from the highest.

**How is range written?**

One way to write the range of a graph is by using interval notation. We start from the bottom and write the intervals that y is defined on. Use brackets, [], when the endpoints are included and parentheses, (), when the endpoints are excluded.

## Is root 2 a natural number?

Because √2 is not an integer (2 is not a perfect square), √2 must therefore be irrational. This proof can be generalized to show that any square root of any natural number that is not a perfect square is irrational.

**Is root 2 a terminating decimal?**

∴ Decimal Expansion of √2 is Non Terminating non repeating.