Solve 4*(-4)+6*(-4)+2*(-8)/sqrt{56*sqrt{98}}

$$\frac { 4 \cdot ( - 4 ) + 6 \cdot ( - 4 ) + 2 \cdot ( - 8 ) } { \sqrt { 56 } \cdot \sqrt { 98 } }$$

Evaluate

$$-\frac{2\sqrt{7}}{7}\approx -0.755928946$$

Solution Steps

Multiply 4 and -4 to get -16. Multiply 6 and -4 to get -24. Multiply 2 and -8 to get -16.

$$\frac{-16-24-16}{\sqrt{56}\sqrt{98}}$$

Subtract 24 from -16 to get -40.

$$\frac{-40-16}{\sqrt{56}\sqrt{98}}$$

Subtract 16 from -40 to get -56.

$$\frac{-56}{\sqrt{56}\sqrt{98}}$$

Factor 56=2^{2}\times 14. Rewrite the square root of the product \sqrt{2^{2}\times 14} as the product of square roots \sqrt{2^{2}}\sqrt{14}. Take the square root of 2^{2}.

$$\frac{-56}{2\sqrt{14}\sqrt{98}}$$

Factor 98=7^{2}\times 2. Rewrite the square root of the product \sqrt{7^{2}\times 2} as the product of square roots \sqrt{7^{2}}\sqrt{2}. Take the square root of 7^{2}.

$$\frac{-56}{2\sqrt{14}\times 7\sqrt{2}}$$

Multiply 2 and 7 to get 14.

$$\frac{-56}{14\sqrt{14}\sqrt{2}}$$

Factor 14=2\times 7. Rewrite the square root of the product \sqrt{2\times 7} as the product of square roots \sqrt{2}\sqrt{7}.

$$\frac{-56}{14\sqrt{2}\sqrt{7}\sqrt{2}}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$\frac{-56}{14\times 2\sqrt{7}}$$

Rationalize the denominator of \frac{-56}{14\times 2\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{-56\sqrt{7}}{14\times 2\left(\sqrt{7}\right)^{2}}$$

The square of \sqrt{7} is 7.

$$\frac{-56\sqrt{7}}{14\times 2\times 7}$$

Cancel out 2\times 14 in both numerator and denominator.

$$\frac{-2\sqrt{7}}{7}$$