How to solve 1/(3 + sqrt(2))

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 1/(3 + sqrt(2)) | Equatix

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Question

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

Evaluate

$\frac{3-\sqrt{2}}{7}\approx 0.22654092$

Solution Steps

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

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

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

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

Square $3$. Square $\sqrt{2}$.

$$\frac{3-\sqrt{2}}{9-2}$$

Subtract $2$ from $9$ to get $7$.

$$\frac{3-\sqrt{2}}{7}$$

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