Yes.
If you set:
3√(2) = (3√(8))/2, and square one side and then the other:
9 x 2 = (9 x 8)/4
18 = 72/4
18 = 18
So, again yes.
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8
root 8 = root 4 x root 2 = 2 root 2, root 18 = root 9 x root 2 = 3 root 2; 2 root 2 x 3 root 2 = 6 x 2 = 12
half of three quarters is 1/2 x 3/4 = 3/8.half of three quarters is 1/2 x 3/4 = 3/8.half of three quarters is 1/2 x 3/4 = 3/8.half of three quarters is 1/2 x 3/4 = 3/8.
The square root of 3 is about 1.73. 1.73 x 8 = 13.84
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.