Question

1 the expression \\(\frac{10}{sqrt{2}}\\) is equivalent to
(1) 5
(2) 20
(3) \\(5sqrt{2}\\)
(4) \\(10sqrt{2}\\)

Explanation:

Step1: Rationalize the denominator

Multiply numerator and denominator by $\sqrt{2}$:
$\frac{10}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{10\sqrt{2}}{\sqrt{2} \times \sqrt{2}}$

Step2: Simplify the denominator

Calculate $\sqrt{2} \times \sqrt{2} = 2$:
$\frac{10\sqrt{2}}{2}$

Step3: Simplify the fraction

Divide 10 by 2:
$5\sqrt{2}$

Answer:

(3) $5\sqrt{2}$