Solve {l}{sqrt{28}+2sqrt{63}}{-10sqrt{7}}

$$\left. \begin{array} { l } { \sqrt { 28 } + 2 \sqrt { 63 } } \\ { - 10 \sqrt { 7 } } \end{array} \right.$$

Evaluate

$$-2\sqrt{7}\approx -5.291502622$$

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}.

$$2\sqrt{7}+2\sqrt{63}-10\sqrt{7}$$

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}.

$$2\sqrt{7}+2\times 3\sqrt{7}-10\sqrt{7}$$

Multiply 2 and 3 to get 6.

$$2\sqrt{7}+6\sqrt{7}-10\sqrt{7}$$

Combine 2\sqrt{7} and 6\sqrt{7} to get 8\sqrt{7}.

$$8\sqrt{7}-10\sqrt{7}$$

Combine 8\sqrt{7} and -10\sqrt{7} to get -2\sqrt{7}.

$$-2\sqrt{7}$$