Solve 2/5*3/7-8^4+sqrt{8}

$$\frac { 2 } { 5 } \times \frac { 3 } { 7 } - 8 ^ { 4 } + \sqrt { 8 }$$

Evaluate

$$2\sqrt{2}-\frac{143354}{35}\approx -4093.000144304$$

Solution Steps

Multiply \frac{2}{5} times \frac{3}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 3}{5\times 7}-8^{4}+\sqrt{8}$$

Do the multiplications in the fraction \frac{2\times 3}{5\times 7}.

$$\frac{6}{35}-8^{4}+\sqrt{8}$$

Calculate 8 to the power of 4 and get 4096.

$$\frac{6}{35}-4096+\sqrt{8}$$

Convert 4096 to fraction \frac{143360}{35}.

$$\frac{6}{35}-\frac{143360}{35}+\sqrt{8}$$

Since \frac{6}{35} and \frac{143360}{35} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6-143360}{35}+\sqrt{8}$$

Subtract 143360 from 6 to get -143354.

$$-\frac{143354}{35}+\sqrt{8}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$-\frac{143354}{35}+2\sqrt{2}$$

Factor

$$\frac{2 {(35 \sqrt{2} - 71677)}}{35} = -4093.0001443038254$$