Solve 5sqrt{3}+6sqrt{50}+3sqrt{48}

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

Evaluate

$$17\sqrt{3}+30\sqrt{2}\approx 71.8712706$$

Solution Steps

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}.

$$5\sqrt{3}+6\times 5\sqrt{2}+3\sqrt{48}$$

Multiply 6 and 5 to get 30.

$$5\sqrt{3}+30\sqrt{2}+3\sqrt{48}$$

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}.

$$5\sqrt{3}+30\sqrt{2}+3\times 4\sqrt{3}$$

Multiply 3 and 4 to get 12.

$$5\sqrt{3}+30\sqrt{2}+12\sqrt{3}$$

Combine 5\sqrt{3} and 12\sqrt{3} to get 17\sqrt{3}.

$$17\sqrt{3}+30\sqrt{2}$$