Solve (-1,3)^2divsqrt{2}4/64-(-1)^3

$$( - 1,3 ) ^ { 2 } \div \sqrt { 2 } \frac { 4 } { 64 } - ( - 1 ) ^ { 3 }$$

Evaluate

$$\frac{169\sqrt{2}}{3200}+1\approx 1.074688154$$

Solution Steps

Calculate -1,3 to the power of 2 and get 1,69.

$$\frac{1,69}{\sqrt{2}}\times \frac{4}{64}-\left(-1\right)^{3}$$

Rationalize the denominator of \frac{1,69}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{1,69\sqrt{2}}{\left(\sqrt{2}\right)^{2}}\times \frac{4}{64}-\left(-1\right)^{3}$$

The square of \sqrt{2} is 2.

$$\frac{1,69\sqrt{2}}{2}\times \frac{4}{64}-\left(-1\right)^{3}$$

Divide 1,69\sqrt{2} by 2 to get 0,845\sqrt{2}.

$$0,845\sqrt{2}\times \frac{4}{64}-\left(-1\right)^{3}$$

Reduce the fraction \frac{4}{64} to lowest terms by extracting and canceling out 4.

$$0,845\sqrt{2}\times \frac{1}{16}-\left(-1\right)^{3}$$

Convert decimal number 0,845 to fraction \frac{845}{1000}. Reduce the fraction \frac{845}{1000} to lowest terms by extracting and canceling out 5.

$$\frac{169}{200}\sqrt{2}\times \frac{1}{16}-\left(-1\right)^{3}$$

Multiply \frac{169}{200} times \frac{1}{16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{169\times 1}{200\times 16}\sqrt{2}-\left(-1\right)^{3}$$

Do the multiplications in the fraction \frac{169\times 1}{200\times 16}.

$$\frac{169}{3200}\sqrt{2}-\left(-1\right)^{3}$$

Calculate -1 to the power of 3 and get -1.

$$\frac{169}{3200}\sqrt{2}-\left(-1\right)$$

The opposite of -1 is 1.

$$\frac{169}{3200}\sqrt{2}+1$$

Factor

$$\frac{169 \sqrt{2} + 3200}{3200} = 1.074688153762829$$