Question

rationalize the denominator of 2/root 3-root 5 rationalize the denominator of 2 divided by root 3 minus root 5

Answer 1

Answer:

Step-by-step explanation:

2

___

root 3-root 5

(we have to multiply both numerator and denominator by root 3+root 5)

then,

(2×root 3)+(2×root 5)

= ________________

3-5

(taking 2 common)

= 2(root 3 +root 5)

____________

-2

= (root 3 +root 5)÷ (-1)

= -root 3 -root 5

Hope it will help

Answer 2

Given: An expression-  $\frac{2}{\sqrt{3} \ - \ \sqrt{5} }$

To find: Rationalized value of the denominator of given expression

Solution:

Considering the expression $\frac{2}{\sqrt{3} \ - \ \sqrt{5} }$,

we know that $(\sqrt{a} +\sqrt{b} )(\sqrt{a} - \sqrt{b}) = a - b$

∵ $(\sqrt{3} - \sqrt{5} )(\sqrt{3} + \sqrt{5} ) = 3 - 5 = -2$ , which is a rational number.

Therefore, to rationalize the denominator of given expression, we need to multiply the numerator and denominator by $(\sqrt{3} + \sqrt{5} )$

⇒ $\frac{2}{\sqrt{3} \ - \sqrt{5} } = \frac{2}{\sqrt{3} \ - \sqrt{5} } \ * \ \frac{\sqrt{3} \ + \ \sqrt{5} }{\sqrt{3} \ + \ \sqrt{5} }$

⇒ $\frac{2(\sqrt{3} \ + \ \sqrt{5}) }{3 \ - \ 5} = \frac{2(\sqrt{3} \ + \ \sqrt{5})}{-2}$

⇒ $- (\sqrt{3} \ + \ \sqrt{5}) = -\sqrt{3} \ - \ \sqrt{5}$

Hence, the rationalized value of the given expression is  $(-\sqrt{3} \ - \ \sqrt{5})$.