Solve 2sqrt{28}+3sqrt{175}-4/sqrt{112}

$$2 \sqrt { 28 } + 3 \sqrt { 175 } - \frac { 4 } { \sqrt { 112 } }$$

Evaluate

$$\frac{132\sqrt{7}}{7}\approx 49.891310437$$

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}.

$$2\times 2\sqrt{7}+3\sqrt{175}-\frac{4}{\sqrt{112}}$$

Multiply 2 and 2 to get 4.

$$4\sqrt{7}+3\sqrt{175}-\frac{4}{\sqrt{112}}$$

Factor 175=5^{2}\times 7. Rewrite the square root of the product \sqrt{5^{2}\times 7} as the product of square roots \sqrt{5^{2}}\sqrt{7}. Take the square root of 5^{2}.

$$4\sqrt{7}+3\times 5\sqrt{7}-\frac{4}{\sqrt{112}}$$

Multiply 3 and 5 to get 15.

$$4\sqrt{7}+15\sqrt{7}-\frac{4}{\sqrt{112}}$$

Combine 4\sqrt{7} and 15\sqrt{7} to get 19\sqrt{7}.

$$19\sqrt{7}-\frac{4}{\sqrt{112}}$$

Factor 112=4^{2}\times 7. Rewrite the square root of the product \sqrt{4^{2}\times 7} as the product of square roots \sqrt{4^{2}}\sqrt{7}. Take the square root of 4^{2}.

$$19\sqrt{7}-\frac{4}{4\sqrt{7}}$$

Rationalize the denominator of \frac{4}{4\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$19\sqrt{7}-\frac{4\sqrt{7}}{4\left(\sqrt{7}\right)^{2}}$$

The square of \sqrt{7} is 7.

$$19\sqrt{7}-\frac{4\sqrt{7}}{4\times 7}$$

Cancel out 4 in both numerator and denominator.

$$19\sqrt{7}-\frac{\sqrt{7}}{7}$$

Combine 19\sqrt{7} and -\frac{\sqrt{7}}{7} to get \frac{132}{7}\sqrt{7}.

$$\frac{132}{7}\sqrt{7}$$