# 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 \$\$.