Solve 4sqrt{50}(10/4)

$$4 \sqrt{ 50 } ( \frac{ 10 }{ 4 } )$$

Evaluate

$$50\sqrt{2}\approx 70.710678119$$

Solution Steps

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}.

$$4\times 5\sqrt{2}\times \frac{10}{4}$$

Multiply 4 and 5 to get 20.

$$20\sqrt{2}\times \frac{10}{4}$$

Reduce the fraction \frac{10}{4} to lowest terms by extracting and canceling out 2.

$$20\sqrt{2}\times \frac{5}{2}$$

Express 20\times \frac{5}{2} as a single fraction.

$$\frac{20\times 5}{2}\sqrt{2}$$

Multiply 20 and 5 to get 100.

$$\frac{100}{2}\sqrt{2}$$

Divide 100 by 2 to get 50.

$$50\sqrt{2}$$