Solve 300*200divsqrt{5}+150*100divsqrt{2}-200*80

$$300 \times 200 \div \sqrt{ 5 } +150 \times 100 \div \sqrt{ 2 } -200 \times 80$$

Evaluate

$$7500\sqrt{2}+12000\sqrt{5}-16000\approx 21439.417447796$$

Solution Steps

Multiply 300 and 200 to get 60000.

$$\frac{60000}{\sqrt{5}}+\frac{150\times 100}{\sqrt{2}}-200\times 80$$

Rationalize the denominator of \frac{60000}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{60000\sqrt{5}}{\left(\sqrt{5}\right)^{2}}+\frac{150\times 100}{\sqrt{2}}-200\times 80$$

The square of \sqrt{5} is 5.

$$\frac{60000\sqrt{5}}{5}+\frac{150\times 100}{\sqrt{2}}-200\times 80$$

Divide 60000\sqrt{5} by 5 to get 12000\sqrt{5}.

$$12000\sqrt{5}+\frac{150\times 100}{\sqrt{2}}-200\times 80$$

Multiply 150 and 100 to get 15000.

$$12000\sqrt{5}+\frac{15000}{\sqrt{2}}-200\times 80$$

Rationalize the denominator of \frac{15000}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$12000\sqrt{5}+\frac{15000\sqrt{2}}{\left(\sqrt{2}\right)^{2}}-200\times 80$$

The square of \sqrt{2} is 2.

$$12000\sqrt{5}+\frac{15000\sqrt{2}}{2}-200\times 80$$

Divide 15000\sqrt{2} by 2 to get 7500\sqrt{2}.

$$12000\sqrt{5}+7500\sqrt{2}-200\times 80$$

Multiply 200 and 80 to get 16000.

$$12000\sqrt{5}+7500\sqrt{2}-16000$$

Factor

$$500 {(15 \sqrt{2} + 24 \sqrt{5} - 32)} = 21439.417447796$$