Solve 2sqrt{28}-5sqrt{63}+sqrt{216}

$$2 \sqrt { 28 } - 5 \sqrt { 63 } + \sqrt { 216 }$$

Evaluate

$$6\sqrt{6}-11\sqrt{7}\approx -14.406325965$$

Solution Steps

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}.

$$2\times 2\sqrt{7}-5\sqrt{63}+\sqrt{216}$$

Multiply 2 and 2 to get 4.

$$4\sqrt{7}-5\sqrt{63}+\sqrt{216}$$

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}.

$$4\sqrt{7}-5\times 3\sqrt{7}+\sqrt{216}$$

Multiply -5 and 3 to get -15.

$$4\sqrt{7}-15\sqrt{7}+\sqrt{216}$$

Combine 4\sqrt{7} and -15\sqrt{7} to get -11\sqrt{7}.

$$-11\sqrt{7}+\sqrt{216}$$

Factor 216=6^{2}\times 6. Rewrite the square root of the product \sqrt{6^{2}\times 6} as the product of square roots \sqrt{6^{2}}\sqrt{6}. Take the square root of 6^{2}.

$$-11\sqrt{7}+6\sqrt{6}$$