Solve (2sqrt{15}*sqrt{30})divsqrt{2}

$$(2 \sqrt{ 15 } \times \sqrt{ 30 } ) \div \sqrt{ 2 }$$

Evaluate

$$30$$

Solution Steps

Factor 30=15\times 2. Rewrite the square root of the product \sqrt{15\times 2} as the product of square roots \sqrt{15}\sqrt{2}.

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

Multiply \sqrt{15} and \sqrt{15} to get 15.

$$\frac{2\times 15\sqrt{2}}{\sqrt{2}}$$

Multiply 2 and 15 to get 30.

$$\frac{30\sqrt{2}}{\sqrt{2}}$$

Rationalize the denominator of \frac{30\sqrt{2}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{30\sqrt{2}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{30\sqrt{2}\sqrt{2}}{2}$$

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

$$\frac{30\times 2}{2}$$

Multiply 30 and 2 to get 60.

$$\frac{60}{2}$$

Divide 60 by 2 to get 30.

$$30$$

Factor

$$2\times 3\times 5$$