Solve (sqrt{75}:sqrt{3}-sqrt{8}:sqrt{2})*(sqrt{2^2*3^4}-5*sqrt{9})-2*(sqrt{40}:sqrt{10}+1)

$$( \sqrt { 75 } : \sqrt { 3 } - \sqrt { 8 } : \sqrt { 2 } ) \times ( \sqrt { 2 ^ { 2 } \times 3 ^ { 4 } } - 5 \times \sqrt { 9 } ) - 2 \times ( \sqrt { 40 } : \sqrt { 10 } + 1 )$$

Evaluate

$$3$$

Solution Steps

Rewrite the division of square roots \frac{\sqrt{75}}{\sqrt{3}} as the square root of the division \sqrt{\frac{75}{3}} and perform the division.

$$\left(\sqrt{25}-\frac{\sqrt{8}}{\sqrt{2}}\right)\left(\sqrt{2^{2}\times 3^{4}}-5\sqrt{9}\right)-2\left(\frac{\sqrt{40}}{\sqrt{10}}+1\right)$$

Calculate the square root of 25 and get 5.

$$\left(5-\frac{\sqrt{8}}{\sqrt{2}}\right)\left(\sqrt{2^{2}\times 3^{4}}-5\sqrt{9}\right)-2\left(\frac{\sqrt{40}}{\sqrt{10}}+1\right)$$

Rewrite the division of square roots \frac{\sqrt{8}}{\sqrt{2}} as the square root of the division \sqrt{\frac{8}{2}} and perform the division.

$$\left(5-\sqrt{4}\right)\left(\sqrt{2^{2}\times 3^{4}}-5\sqrt{9}\right)-2\left(\frac{\sqrt{40}}{\sqrt{10}}+1\right)$$

Calculate the square root of 4 and get 2.

$$\left(5-2\right)\left(\sqrt{2^{2}\times 3^{4}}-5\sqrt{9}\right)-2\left(\frac{\sqrt{40}}{\sqrt{10}}+1\right)$$

Subtract 2 from 5 to get 3.

$$3\left(\sqrt{2^{2}\times 3^{4}}-5\sqrt{9}\right)-2\left(\frac{\sqrt{40}}{\sqrt{10}}+1\right)$$

Calculate 2 to the power of 2 and get 4.

$$3\left(\sqrt{4\times 3^{4}}-5\sqrt{9}\right)-2\left(\frac{\sqrt{40}}{\sqrt{10}}+1\right)$$

Calculate 3 to the power of 4 and get 81.

$$3\left(\sqrt{4\times 81}-5\sqrt{9}\right)-2\left(\frac{\sqrt{40}}{\sqrt{10}}+1\right)$$

Multiply 4 and 81 to get 324.

$$3\left(\sqrt{324}-5\sqrt{9}\right)-2\left(\frac{\sqrt{40}}{\sqrt{10}}+1\right)$$

Calculate the square root of 324 and get 18.

$$3\left(18-5\sqrt{9}\right)-2\left(\frac{\sqrt{40}}{\sqrt{10}}+1\right)$$

Calculate the square root of 9 and get 3.

$$3\left(18-5\times 3\right)-2\left(\frac{\sqrt{40}}{\sqrt{10}}+1\right)$$

Multiply -5 and 3 to get -15.

$$3\left(18-15\right)-2\left(\frac{\sqrt{40}}{\sqrt{10}}+1\right)$$

Subtract 15 from 18 to get 3.

$$3\times 3-2\left(\frac{\sqrt{40}}{\sqrt{10}}+1\right)$$

Multiply 3 and 3 to get 9.

$$9-2\left(\frac{\sqrt{40}}{\sqrt{10}}+1\right)$$

Rewrite the division of square roots \frac{\sqrt{40}}{\sqrt{10}} as the square root of the division \sqrt{\frac{40}{10}} and perform the division.

$$9-2\left(\sqrt{4}+1\right)$$

Calculate the square root of 4 and get 2.

$$9-2\left(2+1\right)$$

Add 2 and 1 to get 3.

$$9-2\times 3$$

Multiply 2 and 3 to get 6.

$$9-6$$

Subtract 6 from 9 to get 3.

$$3$$

Factor

$$3$$