Solve sqrt{775*4*3000div3.14+(152+(15*2))^1}=

$$\sqrt { 775 \times 4 \times 3000 \div 3.14 + ( 152 + ( 15 \times 2 ) ) ^ { 1 } } =$$

Evaluate

$$\frac{\sqrt{73009486118}}{157}\approx 1721.036152871$$

Solution Steps

Multiply 775 and 4 to get 3100.

$$\sqrt{\frac{3100\times 3000}{3.14}+\left(152+15\times 2\right)^{1}}$$

Multiply 3100 and 3000 to get 9300000.

$$\sqrt{\frac{9300000}{3.14}+\left(152+15\times 2\right)^{1}}$$

Expand \frac{9300000}{3.14} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{930000000}{314}+\left(152+15\times 2\right)^{1}}$$

Reduce the fraction \frac{930000000}{314} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{465000000}{157}+\left(152+15\times 2\right)^{1}}$$

Multiply 15 and 2 to get 30.

$$\sqrt{\frac{465000000}{157}+\left(152+30\right)^{1}}$$

Add 152 and 30 to get 182.

$$\sqrt{\frac{465000000}{157}+182^{1}}$$

Calculate 182 to the power of 1 and get 182.

$$\sqrt{\frac{465000000}{157}+182}$$

Add \frac{465000000}{157} and 182 to get \frac{465028574}{157}.

$$\sqrt{\frac{465028574}{157}}$$

Rewrite the square root of the division \sqrt{\frac{465028574}{157}} as the division of square roots \frac{\sqrt{465028574}}{\sqrt{157}}.

$$\frac{\sqrt{465028574}}{\sqrt{157}}$$

Rationalize the denominator of \frac{\sqrt{465028574}}{\sqrt{157}} by multiplying numerator and denominator by \sqrt{157}.

$$\frac{\sqrt{465028574}\sqrt{157}}{\left(\sqrt{157}\right)^{2}}$$

The square of \sqrt{157} is 157.

$$\frac{\sqrt{465028574}\sqrt{157}}{157}$$

To multiply \sqrt{465028574} and \sqrt{157}, multiply the numbers under the square root.

$$\frac{\sqrt{73009486118}}{157}$$