Solve 5*sqrt{75}-8*sqrt{48}+3*sqrt{27}=

$$5 \cdot \sqrt { 75 } - 8 \cdot \sqrt { 48 } + 3 \cdot \sqrt { 27 } =$$

Evaluate

$$2\sqrt{3}\approx 3.464101615$$

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}.

$$5\times 5\sqrt{3}-8\sqrt{48}+3\sqrt{27}$$

Multiply 5 and 5 to get 25.

$$25\sqrt{3}-8\sqrt{48}+3\sqrt{27}$$

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}.

$$25\sqrt{3}-8\times 4\sqrt{3}+3\sqrt{27}$$

Multiply -8 and 4 to get -32.

$$25\sqrt{3}-32\sqrt{3}+3\sqrt{27}$$

Combine 25\sqrt{3} and -32\sqrt{3} to get -7\sqrt{3}.

$$-7\sqrt{3}+3\sqrt{27}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$-7\sqrt{3}+3\times 3\sqrt{3}$$

Multiply 3 and 3 to get 9.

$$-7\sqrt{3}+9\sqrt{3}$$

Combine -7\sqrt{3} and 9\sqrt{3} to get 2\sqrt{3}.

$$2\sqrt{3}$$