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How an irrational number is estimated depends on the nature of the number. The reason for estimating them is that two of the most important numbers in mathematics: pi in geometry and e in calculus, are both irrational. Also, the diagonal of a unit square is of length sqrt(2), an irrational. Irrational Numbers crop up everywhere: there are more irrational numbers than there are rational.

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Q: How do you estimate an irrational number and why do you need for?

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If you want to use a rational number for a mathematical operation, it will be necessary to estimate it for a numerical outcome. Irrational numbers can't be written out exactly.

The number of s.f or rounding off

None, since 57 is NOT an irrational number.

It can be but need not be.

The question cannot be answered because it is based on a false premise.The product of a (not an!) rational number and an irrational number need not be irrational. For eample, the product ofthe rational number, 0, and the irrational number, pi, is 0. The product is rational, not irrational!

No, because if need be it can be expressed as a fraction whereas irrational numbers can't be expressed as fractions.

An irrational number has a never-ending decimal expansion. To estimate it's value, you'd just state the expansion to some number of digits. Ex: sqrt(2) is approximately 1.4142135623730950488 pi is approximately 3.14159265358979323846

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

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

No. For example, -root(2) + root(2) is zero, which is rational.Note that MOST calculations involving irrational numbers give you an irrational number, but there are a few exceptions.

rational * irrational = irrational.

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

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