Solve sqrt{72}-48/sqrt{50}-45/sqrt{128}+2sqrt{98}

$$\sqrt { 72 } - \frac { 48 } { \sqrt { 50 } } - \frac { 45 } { \sqrt { 128 } } + 2 \sqrt { 98 }$$

Evaluate

$$\frac{991\sqrt{2}}{80}\approx 17.518570504$$

Solution Steps

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

$$6\sqrt{2}-\frac{48}{\sqrt{50}}-\frac{45}{\sqrt{128}}+2\sqrt{98}$$

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$6\sqrt{2}-\frac{48}{5\sqrt{2}}-\frac{45}{\sqrt{128}}+2\sqrt{98}$$

Rationalize the denominator of \frac{48}{5\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$6\sqrt{2}-\frac{48\sqrt{2}}{5\left(\sqrt{2}\right)^{2}}-\frac{45}{\sqrt{128}}+2\sqrt{98}$$

The square of \sqrt{2} is 2.

$$6\sqrt{2}-\frac{48\sqrt{2}}{5\times 2}-\frac{45}{\sqrt{128}}+2\sqrt{98}$$

Cancel out 2 in both numerator and denominator.

$$6\sqrt{2}-\frac{24\sqrt{2}}{5}-\frac{45}{\sqrt{128}}+2\sqrt{98}$$

Combine 6\sqrt{2} and -\frac{24\sqrt{2}}{5} to get \frac{6}{5}\sqrt{2}.

$$\frac{6}{5}\sqrt{2}-\frac{45}{\sqrt{128}}+2\sqrt{98}$$

Factor 128=8^{2}\times 2. Rewrite the square root of the product \sqrt{8^{2}\times 2} as the product of square roots \sqrt{8^{2}}\sqrt{2}. Take the square root of 8^{2}.

$$\frac{6}{5}\sqrt{2}-\frac{45}{8\sqrt{2}}+2\sqrt{98}$$

Rationalize the denominator of \frac{45}{8\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{6}{5}\sqrt{2}-\frac{45\sqrt{2}}{8\left(\sqrt{2}\right)^{2}}+2\sqrt{98}$$

The square of \sqrt{2} is 2.

$$\frac{6}{5}\sqrt{2}-\frac{45\sqrt{2}}{8\times 2}+2\sqrt{98}$$

Multiply 8 and 2 to get 16.

$$\frac{6}{5}\sqrt{2}-\frac{45\sqrt{2}}{16}+2\sqrt{98}$$

Combine \frac{6}{5}\sqrt{2} and -\frac{45\sqrt{2}}{16} to get -\frac{129}{80}\sqrt{2}.

$$-\frac{129}{80}\sqrt{2}+2\sqrt{98}$$

Factor 98=7^{2}\times 2. Rewrite the square root of the product \sqrt{7^{2}\times 2} as the product of square roots \sqrt{7^{2}}\sqrt{2}. Take the square root of 7^{2}.

$$-\frac{129}{80}\sqrt{2}+2\times 7\sqrt{2}$$

Multiply 2 and 7 to get 14.

$$-\frac{129}{80}\sqrt{2}+14\sqrt{2}$$

Combine -\frac{129}{80}\sqrt{2} and 14\sqrt{2} to get \frac{991}{80}\sqrt{2}.

$$\frac{991}{80}\sqrt{2}$$