Solve sqrt{75}*sqrt{243}

$$\sqrt { 75 } \cdot \sqrt { 243 }$$

Evaluate

$$135$$

Solution Steps

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

$$5\sqrt{3}\sqrt{243}$$

Factor 243=9^{2}\times 3. Rewrite the square root of the product \sqrt{9^{2}\times 3} as the product of square roots \sqrt{9^{2}}\sqrt{3}. Take the square root of 9^{2}.

$$5\sqrt{3}\times 9\sqrt{3}$$

Multiply 5 and 9 to get 45.

$$45\sqrt{3}\sqrt{3}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$45\times 3$$

Multiply 45 and 3 to get 135.

$$135$$

Factor

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