Solve +4sqrt{2}quad(2)sqrt{31/16*214/25}divsqrt{51/16*234/81}

$$+ 4 \sqrt { 2 } \quad ( 2 ) \sqrt { 3 \frac { 1 } { 16 } \times 2 \frac { 14 } { 25 } } \div \sqrt { 5 \frac { 1 } { 16 } \times 2 \frac { 34 } { 81 } }$$

Evaluate

$$\frac{32\sqrt{2}}{5}\approx 9.050966799$$

Solution Steps

Multiply 4 and 2 to get 8.

$$\frac{8\sqrt{2}\sqrt{\frac{3\times 16+1}{16}\times \frac{2\times 25+14}{25}}}{\sqrt{\frac{5\times 16+1}{16}\times \frac{2\times 81+34}{81}}}$$

Multiply 3 and 16 to get 48.

$$\frac{8\sqrt{2}\sqrt{\frac{48+1}{16}\times \frac{2\times 25+14}{25}}}{\sqrt{\frac{5\times 16+1}{16}\times \frac{2\times 81+34}{81}}}$$

Add 48 and 1 to get 49.

$$\frac{8\sqrt{2}\sqrt{\frac{49}{16}\times \frac{2\times 25+14}{25}}}{\sqrt{\frac{5\times 16+1}{16}\times \frac{2\times 81+34}{81}}}$$

Multiply 2 and 25 to get 50.

$$\frac{8\sqrt{2}\sqrt{\frac{49}{16}\times \frac{50+14}{25}}}{\sqrt{\frac{5\times 16+1}{16}\times \frac{2\times 81+34}{81}}}$$

Add 50 and 14 to get 64.

$$\frac{8\sqrt{2}\sqrt{\frac{49}{16}\times \frac{64}{25}}}{\sqrt{\frac{5\times 16+1}{16}\times \frac{2\times 81+34}{81}}}$$

Multiply \frac{49}{16} times \frac{64}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8\sqrt{2}\sqrt{\frac{49\times 64}{16\times 25}}}{\sqrt{\frac{5\times 16+1}{16}\times \frac{2\times 81+34}{81}}}$$

Do the multiplications in the fraction \frac{49\times 64}{16\times 25}.

$$\frac{8\sqrt{2}\sqrt{\frac{3136}{400}}}{\sqrt{\frac{5\times 16+1}{16}\times \frac{2\times 81+34}{81}}}$$

Reduce the fraction \frac{3136}{400} to lowest terms by extracting and canceling out 16.

$$\frac{8\sqrt{2}\sqrt{\frac{196}{25}}}{\sqrt{\frac{5\times 16+1}{16}\times \frac{2\times 81+34}{81}}}$$

Rewrite the square root of the division \frac{196}{25} as the division of square roots \frac{\sqrt{196}}{\sqrt{25}}. Take the square root of both numerator and denominator.

$$\frac{8\sqrt{2}\times \frac{14}{5}}{\sqrt{\frac{5\times 16+1}{16}\times \frac{2\times 81+34}{81}}}$$

Express 8\times \frac{14}{5} as a single fraction.

$$\frac{\frac{8\times 14}{5}\sqrt{2}}{\sqrt{\frac{5\times 16+1}{16}\times \frac{2\times 81+34}{81}}}$$

Multiply 8 and 14 to get 112.

$$\frac{\frac{112}{5}\sqrt{2}}{\sqrt{\frac{5\times 16+1}{16}\times \frac{2\times 81+34}{81}}}$$

Multiply 5 and 16 to get 80.

$$\frac{\frac{112}{5}\sqrt{2}}{\sqrt{\frac{80+1}{16}\times \frac{2\times 81+34}{81}}}$$

Add 80 and 1 to get 81.

$$\frac{\frac{112}{5}\sqrt{2}}{\sqrt{\frac{81}{16}\times \frac{2\times 81+34}{81}}}$$

Multiply 2 and 81 to get 162.

$$\frac{\frac{112}{5}\sqrt{2}}{\sqrt{\frac{81}{16}\times \frac{162+34}{81}}}$$

Add 162 and 34 to get 196.

$$\frac{\frac{112}{5}\sqrt{2}}{\sqrt{\frac{81}{16}\times \frac{196}{81}}}$$

Multiply \frac{81}{16} times \frac{196}{81} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{112}{5}\sqrt{2}}{\sqrt{\frac{81\times 196}{16\times 81}}}$$

Cancel out 81 in both numerator and denominator.

$$\frac{\frac{112}{5}\sqrt{2}}{\sqrt{\frac{196}{16}}}$$

Reduce the fraction \frac{196}{16} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{112}{5}\sqrt{2}}{\sqrt{\frac{49}{4}}}$$

Rewrite the square root of the division \frac{49}{4} as the division of square roots \frac{\sqrt{49}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$\frac{\frac{112}{5}\sqrt{2}}{\frac{7}{2}}$$

Divide \frac{112}{5}\sqrt{2} by \frac{7}{2} by multiplying \frac{112}{5}\sqrt{2} by the reciprocal of \frac{7}{2}.

$$\frac{\frac{112}{5}\sqrt{2}\times 2}{7}$$

Express \frac{112}{5}\times 2 as a single fraction.

$$\frac{\frac{112\times 2}{5}\sqrt{2}}{7}$$

Multiply 112 and 2 to get 224.

$$\frac{\frac{224}{5}\sqrt{2}}{7}$$

Divide \frac{224}{5}\sqrt{2} by 7 to get \frac{32}{5}\sqrt{2}.

$$\frac{32}{5}\sqrt{2}$$