Solve 6sqrt{45}div3sqrt{30}

$$6 \sqrt { 45 } \div 3 \sqrt { 30 }$$

Evaluate

$$30\sqrt{6}\approx 73.484692283$$

Solution Steps

Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.

$$\frac{6\times 3\sqrt{5}}{3}\sqrt{30}$$

Multiply 6 and 3 to get 18.

$$\frac{18\sqrt{5}}{3}\sqrt{30}$$

Divide 18\sqrt{5} by 3 to get 6\sqrt{5}.

$$6\sqrt{5}\sqrt{30}$$

Factor 30=5\times 6. Rewrite the square root of the product \sqrt{5\times 6} as the product of square roots \sqrt{5}\sqrt{6}.

$$6\sqrt{5}\sqrt{5}\sqrt{6}$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$6\times 5\sqrt{6}$$

Multiply 6 and 5 to get 30.

$$30\sqrt{6}$$