Solve (frac{sqrt{12^2+5^2}}{26}+sqrt[3]{-8}+sqrt{(-1)^2})*(-sqrt{64})

$$( \frac { \sqrt { 12 ^ { 2 } + 5 ^ { 2 } } } { 26 } + \sqrt[ 3 ] { - 8 } + \sqrt { ( - 1 ) ^ { 2 } } ) \times ( - \sqrt { 64 } )$$

Evaluate

$$4$$

Solution Steps

Calculate 12 to the power of 2 and get 144.

$$\left(\frac{\sqrt{144+5^{2}}}{26}+\sqrt[3]{-8}+\sqrt{\left(-1\right)^{2}}\right)\left(-\sqrt{64}\right)$$

Calculate 5 to the power of 2 and get 25.

$$\left(\frac{\sqrt{144+25}}{26}+\sqrt[3]{-8}+\sqrt{\left(-1\right)^{2}}\right)\left(-\sqrt{64}\right)$$

Add 144 and 25 to get 169.

$$\left(\frac{\sqrt{169}}{26}+\sqrt[3]{-8}+\sqrt{\left(-1\right)^{2}}\right)\left(-\sqrt{64}\right)$$

Calculate the square root of 169 and get 13.

$$\left(\frac{13}{26}+\sqrt[3]{-8}+\sqrt{\left(-1\right)^{2}}\right)\left(-\sqrt{64}\right)$$

Reduce the fraction \frac{13}{26} to lowest terms by extracting and canceling out 13.

$$\left(\frac{1}{2}+\sqrt[3]{-8}+\sqrt{\left(-1\right)^{2}}\right)\left(-\sqrt{64}\right)$$

Calculate \sqrt[3]{-8} and get -2.

$$\left(\frac{1}{2}-2+\sqrt{\left(-1\right)^{2}}\right)\left(-\sqrt{64}\right)$$

Subtract 2 from \frac{1}{2} to get -\frac{3}{2}.

$$\left(-\frac{3}{2}+\sqrt{\left(-1\right)^{2}}\right)\left(-\sqrt{64}\right)$$

Calculate -1 to the power of 2 and get 1.

$$\left(-\frac{3}{2}+\sqrt{1}\right)\left(-\sqrt{64}\right)$$

Calculate the square root of 1 and get 1.

$$\left(-\frac{3}{2}+1\right)\left(-\sqrt{64}\right)$$

Add -\frac{3}{2} and 1 to get -\frac{1}{2}.

$$-\frac{1}{2}\left(-\sqrt{64}\right)$$

Calculate the square root of 64 and get 8.

$$-\frac{1}{2}\left(-8\right)$$

Multiply -\frac{1}{2} and -8 to get 4.

$$4$$

Factor

$$2^{2}$$