Solve 5*3sqrt{8}+64div2^23-(65+36div6+33-65)

$$5 \times 3 \sqrt{ 8 } +64 \div { 2 }^{ 23-(65+36 \div 6+33-65) }$$

Evaluate

$$30\sqrt{2}+4194304\approx 4194346.426406872$$

Solution Steps

Multiply 3 and 5 to get 15.

$$15\sqrt{8}+\frac{64}{2^{23-\left(65+\frac{36}{6}+33-65\right)}}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$15\times 2\sqrt{2}+\frac{64}{2^{23-\left(65+\frac{36}{6}+33-65\right)}}$$

Multiply 15 and 2 to get 30.

$$30\sqrt{2}+\frac{64}{2^{23-\left(65+\frac{36}{6}+33-65\right)}}$$

Divide 36 by 6 to get 6.

$$30\sqrt{2}+\frac{64}{2^{23-\left(65+6+33-65\right)}}$$

Add 65 and 6 to get 71.

$$30\sqrt{2}+\frac{64}{2^{23-\left(71+33-65\right)}}$$

Add 71 and 33 to get 104.

$$30\sqrt{2}+\frac{64}{2^{23-\left(104-65\right)}}$$

Subtract 65 from 104 to get 39.

$$30\sqrt{2}+\frac{64}{2^{23-39}}$$

Subtract 39 from 23 to get -16.

$$30\sqrt{2}+\frac{64}{2^{-16}}$$

Calculate 2 to the power of -16 and get \frac{1}{65536}.

$$30\sqrt{2}+\frac{64}{\frac{1}{65536}}$$

Divide 64 by \frac{1}{65536} by multiplying 64 by the reciprocal of \frac{1}{65536}.

$$30\sqrt{2}+64\times 65536$$

Multiply 64 and 65536 to get 4194304.

$$30\sqrt{2}+4194304$$