Evaluate ( square root of 3)/( square root of 26+5)

$\frac{\sqrt{3}}{\sqrt{26} + 5}$

Step 1

Multiply $\frac{\sqrt{3}}{\sqrt{26} + 5}$ by $\frac{\sqrt{26} - 5}{\sqrt{26} - 5}$ .

$\frac{\sqrt{3}}{\sqrt{26} + 5} \cdot \frac{\sqrt{26} - 5}{\sqrt{26} - 5}$

Step 2

Simplify terms.

Multiply $\frac{\sqrt{3}}{\sqrt{26} + 5}$ by $\frac{\sqrt{26} - 5}{\sqrt{26} - 5}$ .

$\frac{\sqrt{3} (\sqrt{26} - 5)}{(\sqrt{26} + 5) (\sqrt{26} - 5)}$

Expand the denominator using the FOIL method.

$\frac{\sqrt{3} (\sqrt{26} - 5)}{{\sqrt{26}}^{2} + \sqrt{26} \cdot - 5 + 5 \sqrt{26} - 25}$

Simplify.

$\frac{\sqrt{3} (\sqrt{26} - 5)}{1}$

Divide $\sqrt{3} (\sqrt{26} - 5)$ by $1$ .

$\sqrt{3} (\sqrt{26} - 5)$

Apply the distributive property.

$\sqrt{3} \sqrt{26} + \sqrt{3} \cdot - 5$

Combine using the product rule for radicals.

$\sqrt{3 \cdot 26} + \sqrt{3} \cdot - 5$

Move $- 5$ to the left of $\sqrt{3}$ .

$\sqrt{3 \cdot 26} - 5 \cdot \sqrt{3}$

Step 3

Multiply $3$ by $26$ .

$\sqrt{78} - 5 \sqrt{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{78} - 5 \sqrt{3}$

Decimal Form:

$0.17150682 \dots$