Solve 9sqrt{7}*5sqrt{14}div21sqrt{2}=

$$9 \sqrt { 7 } \times 5 \sqrt { 14 } \div 21 \sqrt { 2 } =$$

Evaluate

$$30$$

Solution Steps

Factor 14=7\times 2. Rewrite the square root of the product \sqrt{7\times 2} as the product of square roots \sqrt{7}\sqrt{2}.

$$\frac{5\times 9\sqrt{7}\sqrt{7}\sqrt{2}}{21}\sqrt{2}$$

Multiply \sqrt{7} and \sqrt{7} to get 7.

$$\frac{5\times 9\times 7\sqrt{2}}{21}\sqrt{2}$$

Multiply 5 and 9 to get 45.

$$\frac{45\times 7\sqrt{2}}{21}\sqrt{2}$$

Multiply 45 and 7 to get 315.

$$\frac{315\sqrt{2}}{21}\sqrt{2}$$

Divide 315\sqrt{2} by 21 to get 15\sqrt{2}.

$$15\sqrt{2}\sqrt{2}$$

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

$$15\times 2$$

Multiply 15 and 2 to get 30.

$$30$$

Factor

$$2\times 3\times 5$$