Solve 36/sqrt{988*89x}=96

$$\frac{ 36 }{ \sqrt{ 988 } \times 89x } =96$$

Solve for x

$$x=\frac{3\sqrt{247}}{351728}\approx 0.000134049$$

Steps for Solving Linear Equation

Factor 988=2^{2}\times 247. Rewrite the square root of the product \sqrt{2^{2}\times 247} as the product of square roots \sqrt{2^{2}}\sqrt{247}. Take the square root of 2^{2}.

$$\frac{36}{89\times 2\sqrt{247}x}=96$$

Multiply 89 and 2 to get 178.

$$\frac{36}{178\sqrt{247}x}=96$$

Rationalize the denominator of \frac{36}{178\sqrt{247}x} by multiplying numerator and denominator by \sqrt{247}.

$$\frac{36\sqrt{247}}{178\left(\sqrt{247}\right)^{2}x}=96$$

The square of \sqrt{247} is 247.

$$\frac{36\sqrt{247}}{178\times 247x}=96$$

Cancel out 2 in both numerator and denominator.

$$\frac{18\sqrt{247}}{89\times 247x}=96$$

Multiply 89 and 247 to get 21983.

$$\frac{18\sqrt{247}}{21983x}=96$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 21983x.

$$18\sqrt{247}=2110368x$$

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

$$2110368x=18\sqrt{247}$$

Divide both sides by 2110368.

$$\frac{2110368x}{2110368}=\frac{18\sqrt{247}}{2110368}$$

Dividing by 2110368 undoes the multiplication by 2110368.

$$x=\frac{18\sqrt{247}}{2110368}$$

Divide 18\sqrt{247} by 2110368.

$$x=\frac{3\sqrt{247}}{351728}$$