Solve 4sqrt{18}div3sqrt{2}+sqrt{27}sqrt{12}

$$4 \sqrt { 18 } \div 3 \sqrt { 2 } + \sqrt { 27 } \sqrt { 12 }$$

Evaluate

$$26$$

Solution Steps

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$\frac{4\times 3\sqrt{2}}{3}\sqrt{2}+\sqrt{27}\sqrt{12}$$

Multiply 4 and 3 to get 12.

$$\frac{12\sqrt{2}}{3}\sqrt{2}+\sqrt{27}\sqrt{12}$$

Divide 12\sqrt{2} by 3 to get 4\sqrt{2}.

$$4\sqrt{2}\sqrt{2}+\sqrt{27}\sqrt{12}$$

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

$$4\times 2+\sqrt{27}\sqrt{12}$$

Multiply 4 and 2 to get 8.

$$8+\sqrt{27}\sqrt{12}$$

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}.

$$8+3\sqrt{3}\sqrt{12}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$8+3\sqrt{3}\times 2\sqrt{3}$$

Multiply 3 and 2 to get 6.

$$8+6\sqrt{3}\sqrt{3}$$

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

$$8+6\times 3$$

Multiply 6 and 3 to get 18.

$$8+18$$

Add 8 and 18 to get 26.

$$26$$

Factor

$$2\times 13$$