Solve sqrt{21/4*16/81}

$$\sqrt { 2 \frac { 1 } { 4 } \times \frac { 16 } { 81 } }$$

Evaluate

$$\frac{2}{3}\approx 0.666666667$$

Solution Steps

Multiply 2 and 4 to get 8.

$$\sqrt{\frac{8+1}{4}\times \frac{16}{81}}$$

Add 8 and 1 to get 9.

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

Multiply \frac{9}{4} times \frac{16}{81} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{9\times 16}{4\times 81}.

$$\sqrt{\frac{144}{324}}$$

Reduce the fraction \frac{144}{324} to lowest terms by extracting and canceling out 36.

$$\sqrt{\frac{4}{9}}$$

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

$$\frac{2}{3}$$

Factor

$$\frac{2}{3} = 0.6666666666666666$$