Solve 51/5.6*sqrt{5/9.8}

$$\frac { 51 } { 5.6 } \times \sqrt { \frac { 5 } { 9.8 } }$$

Evaluate

$$\frac{1275}{196}\approx 6.505102041$$

Solution Steps

Expand \frac{51}{5.6} by multiplying both numerator and the denominator by 10.

$$\frac{510}{56}\sqrt{\frac{5}{9.8}}$$

Reduce the fraction \frac{510}{56} to lowest terms by extracting and canceling out 2.

$$\frac{255}{28}\sqrt{\frac{5}{9.8}}$$

Expand \frac{5}{9.8} by multiplying both numerator and the denominator by 10.

$$\frac{255}{28}\sqrt{\frac{50}{98}}$$

Reduce the fraction \frac{50}{98} to lowest terms by extracting and canceling out 2.

$$\frac{255}{28}\sqrt{\frac{25}{49}}$$

Rewrite the square root of the division \frac{25}{49} as the division of square roots \frac{\sqrt{25}}{\sqrt{49}}. Take the square root of both numerator and denominator.

$$\frac{255}{28}\times \frac{5}{7}$$

Multiply \frac{255}{28} times \frac{5}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{255\times 5}{28\times 7}$$

Do the multiplications in the fraction \frac{255\times 5}{28\times 7}.

$$\frac{1275}{196}$$

Factor

$$\frac{3 \cdot 17 \cdot 5 ^ {2}}{2 ^ {2} \cdot 7 ^ {2}} = 6\frac{99}{196} = 6.505102040816326$$