Solve 5sqrt{12}-0.5sqrt{48}

$$5 \sqrt{ 12 } -0.5 \sqrt{ 48 }$$

Evaluate

$$8\sqrt{3}\approx 13.856406461$$

Solution Steps

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$5\times 2\sqrt{3}-0.5\sqrt{48}$$

Multiply 5 and 2 to get 10.

$$10\sqrt{3}-0.5\sqrt{48}$$

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}.

$$10\sqrt{3}-0.5\times 4\sqrt{3}$$

Multiply -0.5 and 4 to get -2.

$$10\sqrt{3}-2\sqrt{3}$$

Combine 10\sqrt{3} and -2\sqrt{3} to get 8\sqrt{3}.

$$8\sqrt{3}$$