Solve sqrt{8*5^3+(4*5-0*76)^2}

$$\sqrt { 8 \cdot 5 ^ { 3 } + ( 4 \cdot 5 - 0 \cdot 76 ) ^ { 2 } }$$

Evaluate

$$10\sqrt{14}\approx 37.416573868$$

Solution Steps

Calculate 5 to the power of 3 and get 125.

$$\sqrt{8\times 125+\left(4\times 5-0\times 76\right)^{2}}$$

Multiply 8 and 125 to get 1000.

$$\sqrt{1000+\left(4\times 5-0\times 76\right)^{2}}$$

Multiply 4 and 5 to get 20.

$$\sqrt{1000+\left(20-0\times 76\right)^{2}}$$

Multiply 0 and 76 to get 0.

$$\sqrt{1000+\left(20-0\right)^{2}}$$

Subtract 0 from 20 to get 20.

$$\sqrt{1000+20^{2}}$$

Calculate 20 to the power of 2 and get 400.

$$\sqrt{1000+400}$$

Add 1000 and 400 to get 1400.

$$\sqrt{1400}$$

Factor 1400=10^{2}\times 14. Rewrite the square root of the product \sqrt{10^{2}\times 14} as the product of square roots \sqrt{10^{2}}\sqrt{14}. Take the square root of 10^{2}.

$$10\sqrt{14}$$