Solve sqrt{421/25*2373/81}

$$\sqrt { 4 \frac { 21 } { 25 } \cdot 23 \frac { 73 } { 81 } }$$

Evaluate

$$\frac{484}{45}\approx 10.755555556$$

Solution Steps

Multiply 4 and 25 to get 100.

$$\sqrt{\frac{100+21}{25}\times \frac{23\times 81+73}{81}}$$

Add 100 and 21 to get 121.

$$\sqrt{\frac{121}{25}\times \frac{23\times 81+73}{81}}$$

Multiply 23 and 81 to get 1863.

$$\sqrt{\frac{121}{25}\times \frac{1863+73}{81}}$$

Add 1863 and 73 to get 1936.

$$\sqrt{\frac{121}{25}\times \frac{1936}{81}}$$

Multiply \frac{121}{25} times \frac{1936}{81} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{121\times 1936}{25\times 81}}$$

Do the multiplications in the fraction \frac{121\times 1936}{25\times 81}.

$$\sqrt{\frac{234256}{2025}}$$

Rewrite the square root of the division \frac{234256}{2025} as the division of square roots \frac{\sqrt{234256}}{\sqrt{2025}}. Take the square root of both numerator and denominator.

$$\frac{484}{45}$$

Factor

$$\frac{2 ^ {2} \cdot 11 ^ {2}}{3 ^ {2} \cdot 5} = 10\frac{34}{45} = 10.755555555555556$$