Root of 22

The square root of 22 is approximately 4.6904. Its exact form is √22. Because 22 has no perfect-square factor greater than one, this radical does not simplify to an integer times a smaller integer radical.

Meaning and context

The nearby perfect squares are 16 and 25. Their square roots are four and five, so √22 lies between four and five. Since 22 is closer to 25 than to 16, the value is closer to five.

Examples and usage

For a rough check, 4.69² = 21.9961, which is close to 22. A calculator can supply more decimal places when needed. Keep √22 if the problem requests an exact answer or a simplified radical.

What to check

The expression √22 denotes the nonnegative principal square root. Solving x² = 22 gives two real solutions, ±√22. Do not add a plus-or-minus sign to a principal-root expression unless the task is actually asking for both equation solutions.

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