Solve 15=V/sqrt{48^2+10*5^2}

$$15 = \frac { V } { \sqrt { 48 ^ { 2 } + 10 \cdot 5 ^ { 2 } } }$$

Solve for V

$$V=15\sqrt{2554}\approx 758.05672611$$

Steps for Solving Linear Equation

Calculate 48 to the power of 2 and get 2304.

$$15=\frac{V}{\sqrt{2304+10\times 5^{2}}}$$

Calculate 5 to the power of 2 and get 25.

$$15=\frac{V}{\sqrt{2304+10\times 25}}$$

Multiply 10 and 25 to get 250.

$$15=\frac{V}{\sqrt{2304+250}}$$

Add 2304 and 250 to get 2554.

$$15=\frac{V}{\sqrt{2554}}$$

Rationalize the denominator of \frac{V}{\sqrt{2554}} by multiplying numerator and denominator by \sqrt{2554}.

$$15=\frac{V\sqrt{2554}}{\left(\sqrt{2554}\right)^{2}}$$

The square of \sqrt{2554} is 2554.

$$15=\frac{V\sqrt{2554}}{2554}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{V\sqrt{2554}}{2554}=15$$

Multiply both sides by 2554.

$$V\sqrt{2554}=15\times 2554$$

Multiply 15 and 2554 to get 38310.

$$V\sqrt{2554}=38310$$

The equation is in standard form.

$$\sqrt{2554}V=38310$$

Divide both sides by \sqrt{2554}.

$$\frac{\sqrt{2554}V}{\sqrt{2554}}=\frac{38310}{\sqrt{2554}}$$

Dividing by \sqrt{2554} undoes the multiplication by \sqrt{2554}.

$$V=\frac{38310}{\sqrt{2554}}$$

Divide 38310 by \sqrt{2554}.

$$V=15\sqrt{2554}$$