Solve sqrt{8}*5sqrt{18}

$$\sqrt { 8 } \times 5 \sqrt { 18 }$$

Evaluate

$$60$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$5\times 2\sqrt{2}\sqrt{18}$$

Multiply 5 and 2 to get 10.

$$10\sqrt{2}\sqrt{18}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$10\sqrt{2}\times 3\sqrt{2}$$

Multiply 10 and 3 to get 30.

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

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

$$30\times 2$$

Multiply 30 and 2 to get 60.

$$60$$

Factor

$$2^{2}\times 3\times 5$$