Solve 30-65[(6-3)^2+2(sqrt{700}div5)]+303^3

$$30 - 65 [ ( 6 - 3 ) ^ { 2 } + 2 ( \sqrt { 700 } \div 5 ) ] + 303 ^ { 3 }$$

Evaluate

$$27817572-260\sqrt{7}\approx 27816884.104659121$$

Solution Steps

Subtract 3 from 6 to get 3.

$$30-65\left(3^{2}+2\times \frac{\sqrt{700}}{5}\right)+303^{3}$$

Calculate 3 to the power of 2 and get 9.

$$30-65\left(9+2\times \frac{\sqrt{700}}{5}\right)+303^{3}$$

Factor 700=10^{2}\times 7. Rewrite the square root of the product \sqrt{10^{2}\times 7} as the product of square roots \sqrt{10^{2}}\sqrt{7}. Take the square root of 10^{2}.

$$30-65\left(9+2\times \frac{10\sqrt{7}}{5}\right)+303^{3}$$

Divide 10\sqrt{7} by 5 to get 2\sqrt{7}.

$$30-65\left(9+2\times 2\sqrt{7}\right)+303^{3}$$

Multiply 2 and 2 to get 4.

$$30-65\left(9+4\sqrt{7}\right)+303^{3}$$

Calculate 303 to the power of 3 and get 27818127.

$$30-65\left(9+4\sqrt{7}\right)[phone]$$

Use the distributive property to multiply -65 by 9+4\sqrt{7}.

$$30-585-260\sqrt{7}[phone]$$

Subtract 585 from 30 to get -555.

$$-555-260\sqrt{7}[phone]$$

Add -555 and 27818127 to get 27817572.

$$27817572-260\sqrt{7}$$