Solve 7sqrt{18}+2sqrt{25}-3sqrt{72}

$$7 \sqrt { 18 } + 2 \sqrt { 25 } - 3 \sqrt { 72 }$$

Evaluate

$$3\sqrt{2}+10\approx 14.242640687$$

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}.

$$7\times 3\sqrt{2}+2\sqrt{25}-3\sqrt{72}$$

Multiply 7 and 3 to get 21.

$$21\sqrt{2}+2\sqrt{25}-3\sqrt{72}$$

Calculate the square root of 25 and get 5.

$$21\sqrt{2}+2\times 5-3\sqrt{72}$$

Multiply 2 and 5 to get 10.

$$21\sqrt{2}+10-3\sqrt{72}$$

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}.

$$21\sqrt{2}+10-3\times 6\sqrt{2}$$

Multiply -3 and 6 to get -18.

$$21\sqrt{2}+10-18\sqrt{2}$$

Combine 21\sqrt{2} and -18\sqrt{2} to get 3\sqrt{2}.

$$3\sqrt{2}+10$$