Solve sqrt{18}*sqrt{2}-frac{sqrt{27}}{sqrt{3}}

$$\sqrt{ 18 } \times \sqrt{ 2 } - \frac{ \sqrt{ 27 } }{ \sqrt{ 3 } }$$

Evaluate

$$3$$

Solution Steps

Factor 18=2\times 9. Rewrite the square root of the product \sqrt{2\times 9} as the product of square roots \sqrt{2}\sqrt{9}.

$$\sqrt{2}\sqrt{9}\sqrt{2}-\frac{\sqrt{27}}{\sqrt{3}}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$2\sqrt{9}-\frac{\sqrt{27}}{\sqrt{3}}$$

Calculate the square root of 9 and get 3.

$$2\times 3-\frac{\sqrt{27}}{\sqrt{3}}$$

Multiply 2 and 3 to get 6.

$$6-\frac{\sqrt{27}}{\sqrt{3}}$$

Rewrite the division of square roots \frac{\sqrt{27}}{\sqrt{3}} as the square root of the division \sqrt{\frac{27}{3}} and perform the division.

$$6-\sqrt{9}$$

Calculate the square root of 9 and get 3.

$$6-3$$

Subtract 3 from 6 to get 3.

$$3$$

Factor

$$3$$