Solve 18sqrt{72}+2sqrt{98}

$$18 \sqrt { 72 } + 2 \sqrt { 98 }$$

Evaluate

$$122\sqrt{2}\approx 172.53405461$$

Solution Steps

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

$$18\times 6\sqrt{2}+2\sqrt{98}$$

Multiply 18 and 6 to get 108.

$$108\sqrt{2}+2\sqrt{98}$$

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}.

$$108\sqrt{2}+2\times 7\sqrt{2}$$

Multiply 2 and 7 to get 14.

$$108\sqrt{2}+14\sqrt{2}$$

Combine 108\sqrt{2} and 14\sqrt{2} to get 122\sqrt{2}.

$$122\sqrt{2}$$