Solve sqrt{3^2sqrt{9}}+sqrt{10^2-8^2}

$$\sqrt { 3 ^ { 2 } \sqrt { 9 } } + \sqrt { 10 ^ { 2 } - 8 ^ { 2 } }$$

Evaluate

$$3\sqrt{3}+6\approx 11.196152423$$

Solution Steps

Calculate 3 to the power of 2 and get 9.

$$\sqrt{9\sqrt{9}}+\sqrt{10^{2}-8^{2}}$$

Calculate the square root of 9 and get 3.

$$\sqrt{9\times 3}+\sqrt{10^{2}-8^{2}}$$

Multiply 9 and 3 to get 27.

$$\sqrt{27}+\sqrt{10^{2}-8^{2}}$$

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}.

$$3\sqrt{3}+\sqrt{10^{2}-8^{2}}$$

Calculate 10 to the power of 2 and get 100.

$$3\sqrt{3}+\sqrt{100-8^{2}}$$

Calculate 8 to the power of 2 and get 64.

$$3\sqrt{3}+\sqrt{100-64}$$

Subtract 64 from 100 to get 36.

$$3\sqrt{3}+\sqrt{36}$$

Calculate the square root of 36 and get 6.

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