Solve sqrt{9/4}*16/81

$$\sqrt{ \frac{ 9 }{ 4 } } \times \frac{ 16 }{ 81 }$$

Evaluate

$$\frac{8}{27}\approx 0.296296296$$

Solution Steps

Rewrite the square root of the division \frac{9}{4} as the division of square roots \frac{\sqrt{9}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$\frac{3}{2}\times \frac{16}{81}$$

Multiply \frac{3}{2} times \frac{16}{81} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 16}{2\times 81}$$

Do the multiplications in the fraction \frac{3\times 16}{2\times 81}.

$$\frac{48}{162}$$

Reduce the fraction \frac{48}{162} to lowest terms by extracting and canceling out 6.

$$\frac{8}{27}$$

Factor

$$\frac{2 ^ {3}}{3 ^ {3}} = 0.2962962962962963$$