Solve sqrt{98}div3sqrt{18}*8sqrt{2}

$$\sqrt { 98 } \div 3 \sqrt { 18 } \times 8 \sqrt { 2 }$$

Evaluate

$$112\sqrt{2}\approx 158.391918986$$

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}.

$$8\times \frac{\sqrt{98}}{3}\sqrt{2}\sqrt{9}\sqrt{2}$$

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

$$8\times \frac{\sqrt{98}}{3}\times 2\sqrt{9}$$

Factor 98=7^{2}\times 2. Rewrite the square root of the product \sqrt{7^{2}\times 2} as the product of square roots \sqrt{7^{2}}\sqrt{2}. Take the square root of 7^{2}.

$$8\times \frac{7\sqrt{2}}{3}\times 2\sqrt{9}$$

Multiply 8 and 2 to get 16.

$$16\times \frac{7\sqrt{2}}{3}\sqrt{9}$$

Calculate the square root of 9 and get 3.

$$16\times \frac{7\sqrt{2}}{3}\times 3$$

Multiply 16 and 3 to get 48.

$$48\times \frac{7\sqrt{2}}{3}$$

Cancel out 3, the greatest common factor in 48 and 3.

$$16\times 7\sqrt{2}$$

Multiply 16 and 7 to get 112.

$$112\sqrt{2}$$