Solve 3sqrt{2}*sqrt{80}divsqrt{90}

$$3 \sqrt{ 2 } \times \sqrt{ 80 } \div \sqrt{ 90 }$$

Evaluate

$$4$$

Solution Steps

Factor 80=2\times 40. Rewrite the square root of the product \sqrt{2\times 40} as the product of square roots \sqrt{2}\sqrt{40}.

$$\frac{3\sqrt{2}\sqrt{2}\sqrt{40}}{\sqrt{90}}$$

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

$$\frac{3\times 2\sqrt{40}}{\sqrt{90}}$$

Multiply 3 and 2 to get 6.

$$\frac{6\sqrt{40}}{\sqrt{90}}$$

Factor 40=2^{2}\times 10. Rewrite the square root of the product \sqrt{2^{2}\times 10} as the product of square roots \sqrt{2^{2}}\sqrt{10}. Take the square root of 2^{2}.

$$\frac{6\times 2\sqrt{10}}{\sqrt{90}}$$

Multiply 6 and 2 to get 12.

$$\frac{12\sqrt{10}}{\sqrt{90}}$$

Factor 90=3^{2}\times 10. Rewrite the square root of the product \sqrt{3^{2}\times 10} as the product of square roots \sqrt{3^{2}}\sqrt{10}. Take the square root of 3^{2}.

$$\frac{12\sqrt{10}}{3\sqrt{10}}$$

Cancel out 3\sqrt{10} in both numerator and denominator.

$$4$$

Factor

$$2^{2}$$