Finding a square root without a calculator can be done by guessing at the approximate "right" answer then adjusting the guess until the answer squared is close enough to 2 to meet your need. There is however a formal process (Described at Link) which gives the right answer to any degree of accuracy needed.
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4 the way you work this is: 2*(sqrt)2^2 the square root cancels out the exponent, so your left with 2*2
2 square root 2
the square root of 4 is 2 square root 2
The square of any square root is equal to the number itself. For example, the square of the square root of 2 squared is equal to 2. The square root of 10 squared is equal to 10.Similarly, the square of the square root of 2 is equal to 2.
square root of 20 = square root of 4 * square root of 5. square root of 4 = 2, so your answer is 2 square root of 5.