Solve 6sqrt{75}+sqrt{48}-sqrt{50}

$$6 \sqrt{ 75 } + \sqrt{ 48 } - \sqrt{ 50 }$$

Evaluate

$$34\sqrt{3}-5\sqrt{2}\approx 51.818659645$$

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}.

$$6\times 5\sqrt{3}+\sqrt{48}-\sqrt{50}$$

Multiply 6 and 5 to get 30.

$$30\sqrt{3}+\sqrt{48}-\sqrt{50}$$

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

$$30\sqrt{3}+4\sqrt{3}-\sqrt{50}$$

Combine 30\sqrt{3} and 4\sqrt{3} to get 34\sqrt{3}.

$$34\sqrt{3}-\sqrt{50}$$

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}.

$$34\sqrt{3}-5\sqrt{2}$$