Solve 3(sqrt{48}-5sqrt{27})div2sqrt{3}

$$3 ( \sqrt { 48 } - 5 \sqrt { 27 } ) \div 2 \sqrt { 3 }$$

Evaluate

$$-\frac{99}{2}=-49.5$$

Solution Steps

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

$$\frac{3\left(4\sqrt{3}-5\sqrt{27}\right)}{2}\sqrt{3}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$\frac{3\left(4\sqrt{3}-5\times 3\sqrt{3}\right)}{2}\sqrt{3}$$

Multiply -5 and 3 to get -15.

$$\frac{3\left(4\sqrt{3}-15\sqrt{3}\right)}{2}\sqrt{3}$$

Combine 4\sqrt{3} and -15\sqrt{3} to get -11\sqrt{3}.

$$\frac{3\left(-11\right)\sqrt{3}}{2}\sqrt{3}$$

Multiply 3 and -11 to get -33.

$$\frac{-33\sqrt{3}}{2}\sqrt{3}$$

Express \frac{-33\sqrt{3}}{2}\sqrt{3} as a single fraction.

$$\frac{-33\sqrt{3}\sqrt{3}}{2}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{-33\times 3}{2}$$

Multiply -33 and 3 to get -99.

$$\frac{-99}{2}$$

Fraction \frac{-99}{2} can be rewritten as -\frac{99}{2} by extracting the negative sign.

$$-\frac{99}{2}$$

Factor

$$-\frac{99}{2} = -49\frac{1}{2} = -49.5$$