How to solve (5)/(1+sqrt(3))

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve (5)/(1+sqrt(3)) | Equatix

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Question

$$\frac{ 5 }{ 1+ \sqrt{ 3 } }$$

Evaluate

$\frac{5\left(\sqrt{3}-1\right)}{2}\approx 1.830127019$

Solution Steps

Rationalize the denominator of $\frac{5}{1+\sqrt{3}}$ by multiplying numerator and denominator by $1-\sqrt{3}$.

$$\frac{5\left(1-\sqrt{3}\right)}{\left(1+\sqrt{3}\right)\left(1-\sqrt{3}\right)}$$

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

$$\frac{5\left(1-\sqrt{3}\right)}{1^{2}-\left(\sqrt{3}\right)^{2}}$$

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

$$\frac{5\left(1-\sqrt{3}\right)}{1-3}$$

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

$$\frac{5\left(1-\sqrt{3}\right)}{-2}$$

Use the distributive property to multiply $5$ by $1-\sqrt{3}$.

$$\frac{5-5\sqrt{3}}{-2}$$

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