How to solve 1/(sqrt(26) - 1)

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/(sqrt(26) - 1) | Equatix

Basic Math

Pre-Algebra

Algebra

Trigonometry

Calculus

Precalculus

Statistics

Finite Math

Linear Algebra

Chemistry

Question

$$\frac{1}{\sqrt{26}-1}$$

Evaluate

$\frac{\sqrt{26}+1}{25}\approx 0.243960781$

Solution Steps

Rationalize the denominator of $\frac{1}{\sqrt{26}-1}$ by multiplying numerator and denominator by $\sqrt{26}+1$.

$$\frac{\sqrt{26}+1}{\left(\sqrt{26}-1\right)\left(\sqrt{26}+1\right)}$$

Consider $\left(\sqrt{26}-1\right)\left(\sqrt{26}+1\right)$. Multiplication can be transformed into difference of squares using the rule: $\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$.

$$\frac{\sqrt{26}+1}{\left(\sqrt{26}\right)^{2}-1^{2}}$$

Square $\sqrt{26}$. Square $1$.

$$\frac{\sqrt{26}+1}{26-1}$$

Subtract $1$ from $26$ to get $25$.

$$\frac{\sqrt{26}+1}{25}$$

Show Solution