Solve sqrt{27}*sqrt{3}-4quad(2)9sqrt{3}-7sqrt{12}+5sqrt{48}

$$\sqrt { 27 } \times \sqrt { 3 } - 4 \quad ( 2 ) 9 \sqrt { 3 } - 7 \sqrt { 12 } + 5 \sqrt { 48 }$$

Evaluate

$$9-66\sqrt{3}\approx -105.3153533$$

Solution Steps

Factor 27=3\times 9. Rewrite the square root of the product \sqrt{3\times 9} as the product of square roots \sqrt{3}\sqrt{9}.

$$\sqrt{3}\sqrt{9}\sqrt{3}-4\times 9\times 2\sqrt{3}-7\sqrt{12}+5\sqrt{48}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$3\sqrt{9}-4\times 9\times 2\sqrt{3}-7\sqrt{12}+5\sqrt{48}$$

Calculate the square root of 9 and get 3.

$$3\times 3-4\times 9\times 2\sqrt{3}-7\sqrt{12}+5\sqrt{48}$$

Multiply 3 and 3 to get 9.

$$9-4\times 9\times 2\sqrt{3}-7\sqrt{12}+5\sqrt{48}$$

Multiply 4 and 9 to get 36.

$$9-36\times 2\sqrt{3}-7\sqrt{12}+5\sqrt{48}$$

Multiply 36 and 2 to get 72.

$$9-72\sqrt{3}-7\sqrt{12}+5\sqrt{48}$$

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}.

$$9-72\sqrt{3}-7\times 2\sqrt{3}+5\sqrt{48}$$

Multiply -7 and 2 to get -14.

$$9-72\sqrt{3}-14\sqrt{3}+5\sqrt{48}$$

Combine -72\sqrt{3} and -14\sqrt{3} to get -86\sqrt{3}.

$$9-86\sqrt{3}+5\sqrt{48}$$

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}.

$$9-86\sqrt{3}+5\times 4\sqrt{3}$$

Multiply 5 and 4 to get 20.

$$9-86\sqrt{3}+20\sqrt{3}$$

Combine -86\sqrt{3} and 20\sqrt{3} to get -66\sqrt{3}.

$$9-66\sqrt{3}$$