Solve 4x(sqrt{8}x)^2

$$4 x ( \sqrt { 8 } x ) ^ { 2 }$$

Evaluate

$$32x^{3}$$

Solution Steps

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}.

$$4x\times \left(2\sqrt{2}x\right)^{2}$$

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

$$4x\times 2^{2}\left(\sqrt{2}\right)^{2}x^{2}$$

Calculate 2 to the power of 2 and get 4.

$$4x\times 4\left(\sqrt{2}\right)^{2}x^{2}$$

The square of \sqrt{2} is 2.

$$4x\times 4\times 2x^{2}$$

Multiply 4 and 2 to get 8.

$$4x\times 8x^{2}$$

Multiply 4 and 8 to get 32.

$$32xx^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$32x^{3}$$

Expand

$$32x^{3}$$

Solution Steps

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}.

$$4x\times \left(2\sqrt{2}x\right)^{2}$$

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

$$4x\times 2^{2}\left(\sqrt{2}\right)^{2}x^{2}$$

Calculate 2 to the power of 2 and get 4.

$$4x\times 4\left(\sqrt{2}\right)^{2}x^{2}$$

The square of \sqrt{2} is 2.

$$4x\times 4\times 2x^{2}$$

Multiply 4 and 2 to get 8.

$$4x\times 8x^{2}$$

Multiply 4 and 8 to get 32.

$$32xx^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$32x^{3}$$