Solve sqrt{75}*4*3000div3,14+(152+(15*2))^2

$$\sqrt { 75 } \times 4 \times 3000 \div 3,14 + ( 152 + ( 15 \times 2 ) ) ^ { 2 }$$

Evaluate

$$\frac{3000000\sqrt{3}}{157}+33124\approx 66220.512246539$$

Solution Steps

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

$$\frac{5\sqrt{3}\times 4\times 3000}{3,14}+\left(152+15\times 2\right)^{2}$$

Multiply 5 and 4 to get 20.

$$\frac{20\sqrt{3}\times 3000}{3,14}+\left(152+15\times 2\right)^{2}$$

Multiply 20 and 3000 to get 60000.

$$\frac{60000\sqrt{3}}{3,14}+\left(152+15\times 2\right)^{2}$$

Divide 60000\sqrt{3} by 3,14 to get \frac{3000000}{157}\sqrt{3}.

$$\frac{3000000}{157}\sqrt{3}+\left(152+15\times 2\right)^{2}$$

Multiply 15 and 2 to get 30.

$$\frac{3000000}{157}\sqrt{3}+\left(152+30\right)^{2}$$

Add 152 and 30 to get 182.

$$\frac{3000000}{157}\sqrt{3}+182^{2}$$

Calculate 182 to the power of 2 and get 33124.

$$\frac{3000000}{157}\sqrt{3}+33124$$

Factor

$$\frac{4 {(750000 \sqrt{3} + 1300117)}}{157} = 66220.51224653906$$