Solve 7sqrt{45}-4sqrt{20}

$$7 \sqrt { 45 } - 4 \sqrt { 20 }$$

Evaluate

$$13\sqrt{5}\approx 29.068883707$$

Solution Steps

Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.

$$7\times 3\sqrt{5}-4\sqrt{20}$$

Multiply 7 and 3 to get 21.

$$21\sqrt{5}-4\sqrt{20}$$

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$21\sqrt{5}-4\times 2\sqrt{5}$$

Multiply -4 and 2 to get -8.

$$21\sqrt{5}-8\sqrt{5}$$

Combine 21\sqrt{5} and -8\sqrt{5} to get 13\sqrt{5}.

$$13\sqrt{5}$$