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# Why is the location of an irrational number an approximate location?

Updated: 11/1/2022

Wiki User

9y ago

It is not! The square root of 2, for example, is irrational but you can always locate it exactly by using the diagonal of a unit square.

Wiki User

7y ago

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Q: Why is the location of an irrational number an approximate location?
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### What is the cubic root of 231?

6.13579244 (approximate, this is an irrational number)

### How do you express irrational number on a number line?

Simply plot the irrational number at it's approximate location on the number line and label the irrational number. For example, if you were to plot pi on the number line, you would plot it at about 3.14 and label it with "&pi;" (the pi symbol, if it doesn't show up) Another example is if you want to plot the square root of 2 on the number line. You would plot it at around 1.414 and label it with "&radic;2"

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If the simplified form of an expression contains an irrational number and a numerical evaluation is required then it is necessary to use a rational approximation.

### What is the approximate of each irrational?

Every irrational number can be represented by a non-terminating non-repeating decimal. Rounding this decimal representation to a suitable degree will provide a suitable approximation.

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Approximate location of what, exactly?

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An irrational number.

### Is an irrational number plus an irrational number rational?

No. The sum of an irrational number and any other [real] number is irrational.

### The sum of a rational number and an irrational number is?

The sum of a rational and irrational number must be an irrational number.

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No, 3.56 is not an irrational number. 3.56 is rational.

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rational * irrational = irrational.

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### Can you reduce decimals?

No. A number in 'decimal' format is either exact or approximate; there is no reduction needed or possible. A 'decimal' may be approximate if it is irrational (for example, pi, 3.14159...) or repeating (for example, 1/3, which is 0.333333....).