When simplified, what is the value of $\sqrt{3} \times 3^{\frac{1}{2}} + 12 \div 3 \times 2 - 4^{\frac{3}{2}}$?
Simplify the following:
sqrt(3) sqrt(3) + 12/3×2 - 4^(3/2)
Express 12/3×2 as a single fraction.
12/3×2 = (12×2)/3:
sqrt(3) sqrt(3) + (12×2)/3 - 4^(3/2)
In (12×2)/3, divide 12 in the numerator by 3 in the denominator.
12/3 = (3×4)/3 = 4:
sqrt(3) sqrt(3) + 4×2 - 4^(3/2)
Separate the exponent of 4^(3/2) into integer and fractional parts.
4^(3/2) = 4^(2/2 + 1/2) = 4^(2/2)×sqrt(4):
sqrt(3) sqrt(3) + 4×2 - 4^(2/2) sqrt(4)
Any nonzero number divided by itself is one.
2/2 = 1:
sqrt(3) sqrt(3) + 4×2 - 4 sqrt(4)
Combine products of like terms.
sqrt(3) sqrt(3) = 3:
3 + 4×2 - 4 sqrt(4)
Multiply 4 and 2 together.
4×2 = 8:
3 + 8 - 4 sqrt(4)
Evaluate 3 + 8 - 4 sqrt(4).
3 + 8 - 4 sqrt(4) = 3:
= 3 - final answer
