When simplified, what is the value of $\sqrt{3} \times 3^{\frac{1}{2}} + 12 \div 3 \times 2 - 4^{\frac{3}{2}}$?

Guest Apr 7, 2023

#4**0 **

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**

Guest Apr 7, 2023