It's best to use a calculator for this.
Without a calculator, several methods exist; for example, just try out different numbers. Since 2 squared is 4 and 3 squared is 9, the square root of 8 must be between those too. Continue trying with some other numbers - for example, 2.5 squared is 6.25, so you have to go a bit higher.
More efficient (i.e., faster) methods exists as well, but they are all based on iterative procedures - that is, repeating a series of operations over and over again, until you get close enough to the desired result.
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The square root of minus 8 is equal to the square root of 8 times the square root of minus 1, or 2.8284i.
Square Root of 50: 7.0710678118654752440084436210485Square Root of 8: 2.82842712474619009760337744841942.8284271247461900976033774484194+7.0710678118654752440084436210485-------------------------------------------------------------9.8994949366116653416118210694674
The square root of 8 is 2 multiplied by the square root of 2
The square root of 64 is 8
4 square root of 7