Solve 6sqrt{63}-7sqrt{48}+5sqrt{28}-2sqrt{108}

$$6 \sqrt { 63 } - 7 \sqrt { 48 } + 5 \sqrt { 28 } - 2 \sqrt { 108 }$$

Evaluate

$$4\left(7\sqrt{7}-10\sqrt{3}\right)\approx 4.799004407$$

Solution Steps

Factor 63=3^{2}\times 7. Rewrite the square root of the product \sqrt{3^{2}\times 7} as the product of square roots \sqrt{3^{2}}\sqrt{7}. Take the square root of 3^{2}.

$$6\times 3\sqrt{7}-7\sqrt{48}+5\sqrt{28}-2\sqrt{108}$$

Multiply 6 and 3 to get 18.

$$18\sqrt{7}-7\sqrt{48}+5\sqrt{28}-2\sqrt{108}$$

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}.

$$18\sqrt{7}-7\times 4\sqrt{3}+5\sqrt{28}-2\sqrt{108}$$

Multiply -7 and 4 to get -28.

$$18\sqrt{7}-28\sqrt{3}+5\sqrt{28}-2\sqrt{108}$$

Factor 28=2^{2}\times 7. Rewrite the square root of the product \sqrt{2^{2}\times 7} as the product of square roots \sqrt{2^{2}}\sqrt{7}. Take the square root of 2^{2}.

$$18\sqrt{7}-28\sqrt{3}+5\times 2\sqrt{7}-2\sqrt{108}$$

Multiply 5 and 2 to get 10.

$$18\sqrt{7}-28\sqrt{3}+10\sqrt{7}-2\sqrt{108}$$

Combine 18\sqrt{7} and 10\sqrt{7} to get 28\sqrt{7}.

$$28\sqrt{7}-28\sqrt{3}-2\sqrt{108}$$

Factor 108=6^{2}\times 3. Rewrite the square root of the product \sqrt{6^{2}\times 3} as the product of square roots \sqrt{6^{2}}\sqrt{3}. Take the square root of 6^{2}.

$$28\sqrt{7}-28\sqrt{3}-2\times 6\sqrt{3}$$

Multiply -2 and 6 to get -12.

$$28\sqrt{7}-28\sqrt{3}-12\sqrt{3}$$

Combine -28\sqrt{3} and -12\sqrt{3} to get -40\sqrt{3}.

$$28\sqrt{7}-40\sqrt{3}$$