Solve sqrt{8}=30x(1,1^8-1)

$$\sqrt { 8 } = 30 x ( 1,1 ^ { 8 - 1 } )$$

Solve for x

$$x=\frac{\sqrt{2}}{15}\approx 0.094280904$$

Steps for Solving Linear Equation

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$2\sqrt{2}=30x\times 1\times 1^{8-1}$$

Multiply 30 and 1 to get 30.

$$2\sqrt{2}=30x\times 1^{8-1}$$

Subtract 1 from 8 to get 7.

$$2\sqrt{2}=30x\times 1^{7}$$

Calculate 1 to the power of 7 and get 1.

$$2\sqrt{2}=30x\times 1$$

Multiply 30 and 1 to get 30.

$$2\sqrt{2}=30x$$

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

$$30x=2\sqrt{2}$$

Divide both sides by 30.

$$\frac{30x}{30}=\frac{2\sqrt{2}}{30}$$

Dividing by 30 undoes the multiplication by 30.

$$x=\frac{2\sqrt{2}}{30}$$

Divide 2\sqrt{2} by 30.

$$x=\frac{\sqrt{2}}{15}$$