Question

pythagorean theorem and simplifying radicals practice
16 of 32
simplify.

1. \\(\frac{28}{\sqrt{2}}\\)

(there is a box with \\(\sqrt{}\\) and another box before it, and below are buttons with \\(\pm2\\), \\(\pm4\\),..., \\(\pm20\\))

Explanation:

Step1: Rationalize the denominator

Multiply numerator and denominator by $\sqrt{2}$:
$\frac{28}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{28\sqrt{2}}{\sqrt{2} \times \sqrt{2}}$

Step2: Simplify the denominator

$\sqrt{2} \times \sqrt{2} = 2$, so:
$\frac{28\sqrt{2}}{2}$

Step3: Simplify the fraction

Divide 28 by 2:
$14\sqrt{2}$

Answer:

$14\sqrt{2}$ (matching the boxed values: the first box is 14, the second is 2)