Solve 3(sqrt{27}-4/sqrt{2})

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

Evaluate

$$3^{\frac{5}{2}}-6\sqrt{2}\approx 7.103175894$$

Solution Steps

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}.

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

Rationalize the denominator of \frac{4}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

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

Divide 4\sqrt{2} by 2 to get 2\sqrt{2}.

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

Use the distributive property to multiply 3 by 3\sqrt{3}-2\sqrt{2}.

$$9\sqrt{3}+3\left(-2\sqrt{2}\right)$$

Multiply 3 and -1 to get -3.

$$9\sqrt{3}-3\times 2\sqrt{2}$$

Multiply -3 and 2 to get -6.

$$9\sqrt{3}-6\sqrt{2}$$