Solve sqrt{13}*sqrt{2}divsqrt{13}div3sqrt{2}+(sqrt{2}-1)^0

$$\sqrt { 13 } \times \sqrt { 2 } \div \sqrt { 13 } \div 3 \sqrt { 2 } + ( \sqrt { 2 } - 1 ) ^ { 0 }$$

Evaluate

$$\frac{5}{3}\approx 1.666666667$$

Short Solution Steps

Express \frac{\frac{\sqrt{13}\sqrt{2}}{\sqrt{13}}}{3} as a single fraction.

$$\frac{\sqrt{13}\sqrt{2}}{\sqrt{13}\times 3}\sqrt{2}+\left(\sqrt{2}-1\right)^{0}$$

Cancel out \sqrt{13} in both numerator and denominator.

$$\frac{\sqrt{2}}{3}\sqrt{2}+\left(\sqrt{2}-1\right)^{0}$$

Express \frac{\sqrt{2}}{3}\sqrt{2} as a single fraction.

$$\frac{\sqrt{2}\sqrt{2}}{3}+\left(\sqrt{2}-1\right)^{0}$$

Calculate \sqrt{2}-1 to the power of 0 and get 1.

$$\frac{\sqrt{2}\sqrt{2}}{3}+1$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{3}{3}.

$$\frac{\sqrt{2}\sqrt{2}}{3}+\frac{3}{3}$$

Since \frac{\sqrt{2}\sqrt{2}}{3} and \frac{3}{3} have the same denominator, add them by adding their numerators.

$$\frac{\sqrt{2}\sqrt{2}+3}{3}$$

Do the multiplications in \sqrt{2}\sqrt{2}+3.

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

Do the calculations in 2+3.

$$\frac{5}{3}$$

Factor

$$\frac{5}{3} = 1\frac{2}{3} = 1.6666666666666667$$