Solve frac{2sqrt{30}-2sqrt{2}}{2sqrt{2}}-sqrt{3}

$$\frac { 2 \sqrt { 30 } - 2 \sqrt { 2 } } { 2 \sqrt { 2 } } - \sqrt { 3 }$$

Evaluate

$$\sqrt{15}-\sqrt{3}-1\approx 1.140932539$$

Short Solution Steps

Rationalize the denominator of \frac{2\sqrt{30}-2\sqrt{2}}{2\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\left(2\sqrt{30}-2\sqrt{2}\right)\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}-\sqrt{3}$$

The square of \sqrt{2} is 2.

$$\frac{\left(2\sqrt{30}-2\sqrt{2}\right)\sqrt{2}}{2\times 2}-\sqrt{3}$$

Multiply 2 and 2 to get 4.

$$\frac{\left(2\sqrt{30}-2\sqrt{2}\right)\sqrt{2}}{4}-\sqrt{3}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply \sqrt{3} times \frac{4}{4}.

$$\frac{\left(2\sqrt{30}-2\sqrt{2}\right)\sqrt{2}}{4}-\frac{4\sqrt{3}}{4}$$

Since \frac{\left(2\sqrt{30}-2\sqrt{2}\right)\sqrt{2}}{4} and \frac{4\sqrt{3}}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(2\sqrt{30}-2\sqrt{2}\right)\sqrt{2}-4\sqrt{3}}{4}$$

Do the multiplications in \left(2\sqrt{30}-2\sqrt{2}\right)\sqrt{2}-4\sqrt{3}.

$$\frac{4\sqrt{15}-4-4\sqrt{3}}{4}$$

Divide each term of 4\sqrt{15}-4-4\sqrt{3} by 4 to get \sqrt{15}-1-\sqrt{3}.

$$\sqrt{15}-1-\sqrt{3}$$