# What is sqrt 9, sqrt 32

### With a calculator and crooked numbers

With higher roots you will often need the calculator. The calculators work differently, but the most common key combination is this one.

To type in $$ root 4 (625) $$:

4

shift or inf

where small above it: $$ rootn (x) $$

$$625$$

$$=$$

Sometimes irrational numbers come out:

$$ root 6 (8) = 1.41421356237 ... approx 1.41 $$

The name of the key of the nth root looks a little different on each calculator model:

$$ root y (x) $$ or

$$ root x () $$

You cannot represent irrational numbers as fractions. They have an infinite number of decimal places and are not periodic.

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### One task at the end

You can face the following tasks:

Calculate $$ root n 64 $$ for the numbers $$ n = 2,3,5 $$.

You substitute the numbers 2 and 3 and 6 for n one after the other.

- $$ root 2 64 = 8 $$, because $$ 8 ^ 2 = 64 $$
- $$ root 3 64 = 4 $$, because $$ 4 ^ 3 = 64 $$
- $$ root 5 64 approx 2.297 $$, calculated with the pocket calculator

The normal square root is therefore also a $$ n $$ - th root, with $$ n = 2 $$.

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