Solve (sqrt{2}sqrt{70})^2

$$( \sqrt { 2 } \sqrt { 70 } ) ^ { 2 }$$

Evaluate

$$140$$

Solution Steps

Factor 70=2\times 35. Rewrite the square root of the product \sqrt{2\times 35} as the product of square roots \sqrt{2}\sqrt{35}.

$$\left(\sqrt{2}\sqrt{2}\sqrt{35}\right)^{2}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$\left(2\sqrt{35}\right)^{2}$$

Expand \left(2\sqrt{35}\right)^{2}.

$$2^{2}\left(\sqrt{35}\right)^{2}$$

Calculate 2 to the power of 2 and get 4.

$$4\left(\sqrt{35}\right)^{2}$$

The square of \sqrt{35} is 35.

$$4\times 35$$

Multiply 4 and 35 to get 140.

$$140$$

Factor

$$2^{2}\times 5\times 7$$