Solve 3sqrt{23}*2sqrt{3}*sqrt{69}=

$$3 \sqrt { 23 } \cdot 2 \sqrt { 3 } \cdot \sqrt { 69 } =$$

Evaluate

$$414$$

Solution Steps

Factor 69=23\times 3. Rewrite the square root of the product \sqrt{23\times 3} as the product of square roots \sqrt{23}\sqrt{3}.

$$2\times 3\sqrt{23}\sqrt{3}\sqrt{23}\sqrt{3}$$

Multiply \sqrt{23} and \sqrt{23} to get 23.

$$2\times 3\times 23\sqrt{3}\sqrt{3}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$2\times 3\times 23\times 3$$

Multiply 2 and 3 to get 6.

$$6\times 23\times 3$$

Multiply 6 and 23 to get 138.

$$138\times 3$$

Multiply 138 and 3 to get 414.

$$414$$

Factor

$$2\times 3^{2}\times 23$$