Solve sqrt{9^2+9^2+2*9*9*0.5}

$$\sqrt { 9 ^ { 2 } + 9 ^ { 2 } + 2 \times 9 \times 9 \times 0.5 }$$

Evaluate

$$9\sqrt{3}\approx 15.588457268$$

Solution Steps

Calculate 9 to the power of 2 and get 81.

$$\sqrt{81+9^{2}+2\times 9\times 9\times 0.5}$$

Calculate 9 to the power of 2 and get 81.

$$\sqrt{81+81+2\times 9\times 9\times 0.5}$$

Add 81 and 81 to get 162.

$$\sqrt{162+2\times 9\times 9\times 0.5}$$

Multiply 2 and 9 to get 18.

$$\sqrt{162+18\times 9\times 0.5}$$

Multiply 18 and 9 to get 162.

$$\sqrt{162+162\times 0.5}$$

Multiply 162 and 0.5 to get 81.

$$\sqrt{162+81}$$

Add 162 and 81 to get 243.

$$\sqrt{243}$$

Factor 243=9^{2}\times 3. Rewrite the square root of the product \sqrt{9^{2}\times 3} as the product of square roots \sqrt{9^{2}}\sqrt{3}. Take the square root of 9^{2}.

$$9\sqrt{3}$$