Solve (sqrt{9*100*4}-sqrt{625*4}-sqrt{100})*5^2+sqrt{1024:64:4}

$$( \sqrt { 9 \times 100 \times 4 } - \sqrt { 625 \times 4 } - \sqrt { 100 } ) \times 5 ^ { 2 } + \sqrt { 1024 : 64 : 4 }$$

Evaluate

$$2$$

Solution Steps

Multiply 9 and 100 to get 900.

$$\left(\sqrt{900\times 4}-\sqrt{625\times 4}-\sqrt{100}\right)\times 5^{2}+\sqrt{\frac{\frac{1024}{64}}{4}}$$

Multiply 900 and 4 to get 3600.

$$\left(\sqrt{3600}-\sqrt{625\times 4}-\sqrt{100}\right)\times 5^{2}+\sqrt{\frac{\frac{1024}{64}}{4}}$$

Calculate the square root of 3600 and get 60.

$$\left(60-\sqrt{625\times 4}-\sqrt{100}\right)\times 5^{2}+\sqrt{\frac{\frac{1024}{64}}{4}}$$

Multiply 625 and 4 to get 2500.

$$\left(60-\sqrt{2500}-\sqrt{100}\right)\times 5^{2}+\sqrt{\frac{\frac{1024}{64}}{4}}$$

Calculate the square root of 2500 and get 50.

$$\left(60-50-\sqrt{100}\right)\times 5^{2}+\sqrt{\frac{\frac{1024}{64}}{4}}$$

Subtract 50 from 60 to get 10.

$$\left(10-\sqrt{100}\right)\times 5^{2}+\sqrt{\frac{\frac{1024}{64}}{4}}$$

Calculate the square root of 100 and get 10.

$$\left(10-10\right)\times 5^{2}+\sqrt{\frac{\frac{1024}{64}}{4}}$$

Subtract 10 from 10 to get 0.

$$0\times 5^{2}+\sqrt{\frac{\frac{1024}{64}}{4}}$$

Calculate 5 to the power of 2 and get 25.

$$0\times 25+\sqrt{\frac{\frac{1024}{64}}{4}}$$

Multiply 0 and 25 to get 0.

$$0+\sqrt{\frac{\frac{1024}{64}}{4}}$$

Express \frac{\frac{1024}{64}}{4} as a single fraction.

$$0+\sqrt{\frac{1024}{64\times 4}}$$

Multiply 64 and 4 to get 256.

$$0+\sqrt{\frac{1024}{256}}$$

Divide 1024 by 256 to get 4.

$$0+\sqrt{4}$$

Calculate the square root of 4 and get 2.

$$0+2$$

Add 0 and 2 to get 2.

$$2$$

Factor

$$2$$