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.
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.
The square root of the square root of 2
2
The square root of 64 is 8 and you can work it out using the square root algorithm.
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
square root 2 times square root 3 times square root 8
The square root of 2 plus the square root of 2 is equal to twice the square root of 2, therefore the correct answer is: 2(√2) or √8
4
the square root of 4 is 2 square root 2
When you multiply 2 by √2, you are essentially multiplying 2 by 2^(1/2). Using the properties of exponents, when you multiply two numbers with the same base, you add the exponents. Therefore, 2 * 2^(1/2) = 2^(1) * 2^(1/2) = 2^(1 + 1/2) = 2^(3/2). Simplifying this further, 2^(3/2) is equivalent to √(2^3) = √8.
The square root of two times the square root of two equals two
2