Solve 5sqrt{11/3}3sqrt{54}

$$5 \sqrt{ 1 \frac{ 1 }{ 3 } } 3 \sqrt{ 54 }$$

Evaluate

$$90\sqrt{2}\approx 127.279220614$$

Solution Steps

Multiply 3 and 5 to get 15.

$$15\sqrt{\frac{1\times 3+1}{3}}\sqrt{54}$$

Multiply 1 and 3 to get 3.

$$15\sqrt{\frac{3+1}{3}}\sqrt{54}$$

Add 3 and 1 to get 4.

$$15\sqrt{\frac{4}{3}}\sqrt{54}$$

Rewrite the square root of the division \sqrt{\frac{4}{3}} as the division of square roots \frac{\sqrt{4}}{\sqrt{3}}.

$$15\times \frac{\sqrt{4}}{\sqrt{3}}\sqrt{54}$$

Calculate the square root of 4 and get 2.

$$15\times \frac{2}{\sqrt{3}}\sqrt{54}$$

Rationalize the denominator of \frac{2}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$15\times \frac{2\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\sqrt{54}$$

The square of \sqrt{3} is 3.

$$15\times \frac{2\sqrt{3}}{3}\sqrt{54}$$

Factor 54=3^{2}\times 6. Rewrite the square root of the product \sqrt{3^{2}\times 6} as the product of square roots \sqrt{3^{2}}\sqrt{6}. Take the square root of 3^{2}.

$$15\times \frac{2\sqrt{3}}{3}\times 3\sqrt{6}$$

Multiply 15 and 3 to get 45.

$$45\times \frac{2\sqrt{3}}{3}\sqrt{6}$$

Cancel out 3, the greatest common factor in 45 and 3.

$$15\times 2\sqrt{3}\sqrt{6}$$

Multiply 15 and 2 to get 30.

$$30\sqrt{3}\sqrt{6}$$

Factor 6=3\times 2. Rewrite the square root of the product \sqrt{3\times 2} as the product of square roots \sqrt{3}\sqrt{2}.

$$30\sqrt{3}\sqrt{3}\sqrt{2}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$30\times 3\sqrt{2}$$

Multiply 30 and 3 to get 90.

$$90\sqrt{2}$$