Solve 2/(sqrt(3) - 1) 11. Rationalize the denominator : | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$\frac { 2 } { \sqrt { 3 } - 1 }$$

Evaluate

$\sqrt{3}+1\approx 2.732050808$

Solution Steps

Rationalize the denominator of $\frac{2}{\sqrt{3}-1}$ by multiplying numerator and denominator by $\sqrt{3}+1$.

$$\frac{2\left(\sqrt{3}+1\right)}{\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)}$$

Consider $\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)$. Multiplication can be transformed into difference of squares using the rule: $\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$.

$$\frac{2\left(\sqrt{3}+1\right)}{\left(\sqrt{3}\right)^{2}-1^{2}}$$

Square $\sqrt{3}$. Square $1$.

$$\frac{2\left(\sqrt{3}+1\right)}{3-1}$$

Subtract $1$ from $3$ to get $2$.

$$\frac{2\left(\sqrt{3}+1\right)}{2}$$

Cancel out $2$ and $2$.

$$\sqrt{3}+1$$