Solve (sqrt{8}-3sqrt{18})^2

$$( \sqrt { 8 } - 3 \sqrt { 18 } ) ^ { 2 }$$

Evaluate

$$98$$

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}.

$$\left(2\sqrt{2}-3\sqrt{18}\right)^{2}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$\left(2\sqrt{2}-3\times 3\sqrt{2}\right)^{2}$$

Multiply -3 and 3 to get -9.

$$\left(2\sqrt{2}-9\sqrt{2}\right)^{2}$$

Combine 2\sqrt{2} and -9\sqrt{2} to get -7\sqrt{2}.

$$\left(-7\sqrt{2}\right)^{2}$$

Expand \left(-7\sqrt{2}\right)^{2}.

$$\left(-7\right)^{2}\left(\sqrt{2}\right)^{2}$$

Calculate -7 to the power of 2 and get 49.

$$49\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$49\times 2$$

Multiply 49 and 2 to get 98.

$$98$$

Factor

$$2\times 7^{2}$$