Solve {l}{V=sqrt{2*9.8*20}}{U=sqrt{V^2+14^2}}

$$\left. \begin{array} { l } { V = \sqrt { 2 \times 9.8 \times 20 } } \\ { U = \sqrt { V ^ { 2 } + 14 ^ { 2 } } } \end{array} \right.$$

Solve for V, U

$$V=14\sqrt{2}\approx 19.798989873$$

$$U=14\sqrt{3}\approx 24.248711306$$

Solution Steps

Consider the first equation. Multiply 2 and 9.8 to get 19.6.

$$V=\sqrt{19.6\times 20}$$

Multiply 19.6 and 20 to get 392.

$$V=\sqrt{392}$$

Factor 392=14^{2}\times 2. Rewrite the square root of the product \sqrt{14^{2}\times 2} as the product of square roots \sqrt{14^{2}}\sqrt{2}. Take the square root of 14^{2}.

$$V=14\sqrt{2}$$

Consider the second equation. Insert the known values of variables into the equation.

$$U=\sqrt{\left(14\sqrt{2}\right)^{2}+14^{2}}$$

Expand \left(14\sqrt{2}\right)^{2}.

$$U=\sqrt{14^{2}\left(\sqrt{2}\right)^{2}+14^{2}}$$

Calculate 14 to the power of 2 and get 196.

$$U=\sqrt{196\left(\sqrt{2}\right)^{2}+14^{2}}$$

The square of \sqrt{2} is 2.

$$U=\sqrt{196\times 2+14^{2}}$$

Multiply 196 and 2 to get 392.

$$U=\sqrt{392+14^{2}}$$

Calculate 14 to the power of 2 and get 196.

$$U=\sqrt{392+196}$$

Add 392 and 196 to get 588.

$$U=\sqrt{588}$$

Factor 588=14^{2}\times 3. Rewrite the square root of the product \sqrt{14^{2}\times 3} as the product of square roots \sqrt{14^{2}}\sqrt{3}. Take the square root of 14^{2}.

$$U=14\sqrt{3}$$

The system is now solved.

$$V=14\sqrt{2} U=14\sqrt{3}$$