Solve 5sqrt{72}-sqrt{50}

$$5 \sqrt { 72 } - \sqrt { 50 }$$

Evaluate

$$25\sqrt{2}\approx 35.355339059$$

Solution Steps

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

$$5\times 6\sqrt{2}-\sqrt{50}$$

Multiply 5 and 6 to get 30.

$$30\sqrt{2}-\sqrt{50}$$

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$30\sqrt{2}-5\sqrt{2}$$

Combine 30\sqrt{2} and -5\sqrt{2} to get 25\sqrt{2}.

$$25\sqrt{2}$$