Solve 5sqrt{5}+frac{3sqrt{8}}{4sqrt{2}}+(6*5^3)(8*2)=

$$5 \sqrt { 5 } + \frac { 3 \sqrt { 8 } } { 4 \sqrt { 2 } } + ( 6 \times 5 ^ { 3 } ) ( 8 \times 2 ) =$$

Evaluate

$$5\sqrt{5}+\frac{24003}{2}\approx 12012.680339887$$

Solution Steps

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}.

$$5\sqrt{5}+\frac{3\times 2\sqrt{2}}{4\sqrt{2}}+6\times 5^{3}\times 8\times 2$$

Multiply 3 and 2 to get 6.

$$5\sqrt{5}+\frac{6\sqrt{2}}{4\sqrt{2}}+6\times 5^{3}\times 8\times 2$$

Cancel out 2\sqrt{2} in both numerator and denominator.

$$5\sqrt{5}+\frac{3}{2}+6\times 5^{3}\times 8\times 2$$

Calculate 5 to the power of 3 and get 125.

$$5\sqrt{5}+\frac{3}{2}+6\times 125\times 8\times 2$$

Multiply 6 and 125 to get 750.

$$5\sqrt{5}+\frac{3}{2}+750\times 8\times 2$$

Multiply 750 and 8 to get 6000.

$$5\sqrt{5}+\frac{3}{2}+6000\times 2$$

Multiply 6000 and 2 to get 12000.

$$5\sqrt{5}+\frac{3}{2}+12000$$

Convert 12000 to fraction \frac{24000}{2}.

$$5\sqrt{5}+\frac{3}{2}+\frac{24000}{2}$$

Since \frac{3}{2} and \frac{24000}{2} have the same denominator, add them by adding their numerators.

$$5\sqrt{5}+\frac{3+24000}{2}$$

Add 3 and 24000 to get 24003.

$$5\sqrt{5}+\frac{24003}{2}$$

Factor

$$\frac{10 \sqrt{5} + 24003}{2} = 12012.680339887498$$