Solve sqrt{375}*sqrt{27}

$$\sqrt{ 375 } \times \sqrt{ 27 }$$

Evaluate

$$45\sqrt{5}\approx 100.623058987$$

Solution Steps

Factor 375=5^{2}\times 15. Rewrite the square root of the product \sqrt{5^{2}\times 15} as the product of square roots \sqrt{5^{2}}\sqrt{15}. Take the square root of 5^{2}.

$$5\sqrt{15}\sqrt{27}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$5\sqrt{15}\times 3\sqrt{3}$$

Multiply 5 and 3 to get 15.

$$15\sqrt{15}\sqrt{3}$$

Factor 15=3\times 5. Rewrite the square root of the product \sqrt{3\times 5} as the product of square roots \sqrt{3}\sqrt{5}.

$$15\sqrt{3}\sqrt{5}\sqrt{3}$$

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

$$15\times 3\sqrt{5}$$

Multiply 15 and 3 to get 45.

$$45\sqrt{5}$$