Solve 4sqrt{3}2sqrt{50}2sqrt{3/4}

$$4 \sqrt{ 3 } 2 \sqrt{ 50 } 2 \sqrt{ \frac{ 3 }{ 4 } }$$

Evaluate

$$120\sqrt{2}\approx 169.705627485$$

Solution Steps

Multiply 2 and 2 to get 4.

$$4\times 4\sqrt{3}\sqrt{50}\sqrt{\frac{3}{4}}$$

Multiply 4 and 4 to get 16.

$$16\sqrt{3}\sqrt{50}\sqrt{\frac{3}{4}}$$

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$16\sqrt{3}\times 5\sqrt{2}\sqrt{\frac{3}{4}}$$

Multiply 16 and 5 to get 80.

$$80\sqrt{3}\sqrt{2}\sqrt{\frac{3}{4}}$$

Rewrite the square root of the division \sqrt{\frac{3}{4}} as the division of square roots \frac{\sqrt{3}}{\sqrt{4}}.

$$80\sqrt{3}\sqrt{2}\times \frac{\sqrt{3}}{\sqrt{4}}$$

Calculate the square root of 4 and get 2.

$$80\sqrt{3}\sqrt{2}\times \frac{\sqrt{3}}{2}$$

Cancel out 2, the greatest common factor in 80 and 2.

$$40\sqrt{3}\sqrt{3}\sqrt{2}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$40\times 3\sqrt{2}$$

Multiply 40 and 3 to get 120.

$$120\sqrt{2}$$