Solve frac{0sqrt{75}}{sqrt{12}}+frac{sqrt{108}}{sqrt{147}}-sqrt{48}

$$\frac { 0 \sqrt { 75 } } { \sqrt { 12 } } + \frac { \sqrt { 108 } } { \sqrt { 147 } } - \sqrt { 48 }$$

Evaluate

$$\frac{6}{7}-4\sqrt{3}\approx -6.071060373$$

Solution Steps

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

$$\frac{0\times 5\sqrt{3}}{\sqrt{12}}+\frac{\sqrt{108}}{\sqrt{147}}-\sqrt{48}$$

Multiply 0 and 5 to get 0.

$$\frac{0\sqrt{3}}{\sqrt{12}}+\frac{\sqrt{108}}{\sqrt{147}}-\sqrt{48}$$

Anything times zero gives zero.

$$\frac{0}{\sqrt{12}}+\frac{\sqrt{108}}{\sqrt{147}}-\sqrt{48}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$\frac{0}{2\sqrt{3}}+\frac{\sqrt{108}}{\sqrt{147}}-\sqrt{48}$$

Zero divided by any non-zero term gives zero.

$$0+\frac{\sqrt{108}}{\sqrt{147}}-\sqrt{48}$$

Factor 108=6^{2}\times 3. Rewrite the square root of the product \sqrt{6^{2}\times 3} as the product of square roots \sqrt{6^{2}}\sqrt{3}. Take the square root of 6^{2}.

$$0+\frac{6\sqrt{3}}{\sqrt{147}}-\sqrt{48}$$

Factor 147=7^{2}\times 3. Rewrite the square root of the product \sqrt{7^{2}\times 3} as the product of square roots \sqrt{7^{2}}\sqrt{3}. Take the square root of 7^{2}.

$$0+\frac{6\sqrt{3}}{7\sqrt{3}}-\sqrt{48}$$

Cancel out \sqrt{3} in both numerator and denominator.

$$0+\frac{6}{7}-\sqrt{48}$$

Add 0 and \frac{6}{7} to get \frac{6}{7}.

$$\frac{6}{7}-\sqrt{48}$$

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

$$\frac{6}{7}-4\sqrt{3}$$