Solve 4sqrt{7}+sqrt{63}-2sqrt{28}=

$$4 \sqrt { 7 } + \sqrt { 63 } - 2 \sqrt { 28 } =$$

Evaluate

$$3\sqrt{7}\approx 7.937253933$$

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}.

$$4\sqrt{7}+3\sqrt{7}-2\sqrt{28}$$

Combine 4\sqrt{7} and 3\sqrt{7} to get 7\sqrt{7}.

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

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}.

$$7\sqrt{7}-2\times 2\sqrt{7}$$

Multiply -2 and 2 to get -4.

$$7\sqrt{7}-4\sqrt{7}$$

Combine 7\sqrt{7} and -4\sqrt{7} to get 3\sqrt{7}.

$$3\sqrt{7}$$