Solve cvc/5-2sqrt{6}=

$$\frac { c v c } { 5 - 2 \sqrt { 6 } } =$$

Factor

$$\left(2\sqrt{6}+5\right)vc^{2}$$

Solution Steps

Multiply c and c to get c^{2}.

$$factor(\frac{c^{2}v}{5-2\sqrt{6}})$$

Rationalize the denominator of \frac{c^{2}v}{5-2\sqrt{6}} by multiplying numerator and denominator by 5+2\sqrt{6}.

$$factor(\frac{c^{2}v\left(5+2\sqrt{6}\right)}{\left(5-2\sqrt{6}\right)\left(5+2\sqrt{6}\right)})$$

Consider \left(5-2\sqrt{6}\right)\left(5+2\sqrt{6}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$factor(\frac{c^{2}v\left(5+2\sqrt{6}\right)}{5^{2}-\left(-2\sqrt{6}\right)^{2}})$$

Calculate 5 to the power of 2 and get 25.

$$factor(\frac{c^{2}v\left(5+2\sqrt{6}\right)}{25-\left(-2\sqrt{6}\right)^{2}})$$

Expand \left(-2\sqrt{6}\right)^{2}.

$$factor(\frac{c^{2}v\left(5+2\sqrt{6}\right)}{25-\left(-2\right)^{2}\left(\sqrt{6}\right)^{2}})$$

Calculate -2 to the power of 2 and get 4.

$$factor(\frac{c^{2}v\left(5+2\sqrt{6}\right)}{25-4\left(\sqrt{6}\right)^{2}})$$

The square of \sqrt{6} is 6.

$$factor(\frac{c^{2}v\left(5+2\sqrt{6}\right)}{25-4\times 6})$$

Multiply 4 and 6 to get 24.

$$factor(\frac{c^{2}v\left(5+2\sqrt{6}\right)}{25-24})$$

Subtract 24 from 25 to get 1.

$$factor(\frac{c^{2}v\left(5+2\sqrt{6}\right)}{1})$$

Anything divided by one gives itself.

$$factor(c^{2}v\left(5+2\sqrt{6}\right))$$

Use the distributive property to multiply c^{2}v by 5+2\sqrt{6}.

$$factor(5c^{2}v+2c^{2}v\sqrt{6})$$

Factor out c^{2}v.

$$c^{2}v\left(5+2\sqrt{6}\right)$$

Evaluate

$$\left(2\sqrt{6}+5\right)vc^{2}$$