Solve sqrt{63}+2/sqrt{7}-sqrt{28}

$$\sqrt { 63 } + \frac { 2 } { \sqrt { 7 } } - \sqrt { 28 }$$

Evaluate

$$\frac{9\sqrt{7}}{7}\approx 3.401680257$$

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}.

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

Rationalize the denominator of \frac{2}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$3\sqrt{7}+\frac{2\sqrt{7}}{\left(\sqrt{7}\right)^{2}}-\sqrt{28}$$

The square of \sqrt{7} is 7.

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

Combine 3\sqrt{7} and \frac{2\sqrt{7}}{7} to get \frac{23}{7}\sqrt{7}.

$$\frac{23}{7}\sqrt{7}-\sqrt{28}$$

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}.

$$\frac{23}{7}\sqrt{7}-2\sqrt{7}$$

Combine \frac{23}{7}\sqrt{7} and -2\sqrt{7} to get \frac{9}{7}\sqrt{7}.

$$\frac{9}{7}\sqrt{7}$$