Solve -frac{5sqrt{2*5*9.8}}{15}

$$- \frac{ 5 \sqrt{ 2 \times 5 \times 9.8 } }{ 15 }$$

Evaluate

$$-\frac{7\sqrt{2}}{3}\approx -3.299831646$$

Solution Steps

Multiply 2 and 5 to get 10.

$$-\frac{5\sqrt{10\times 9.8}}{15}$$

Multiply 10 and 9.8 to get 98.

$$-\frac{5\sqrt{98}}{15}$$

Factor 98=7^{2}\times 2. Rewrite the square root of the product \sqrt{7^{2}\times 2} as the product of square roots \sqrt{7^{2}}\sqrt{2}. Take the square root of 7^{2}.

$$-\frac{5\times 7\sqrt{2}}{15}$$

Multiply 5 and 7 to get 35.

$$-\frac{35\sqrt{2}}{15}$$

Divide 35\sqrt{2} by 15 to get \frac{7}{3}\sqrt{2}.

$$-\frac{7}{3}\sqrt{2}$$