Question

1divided by root 9-root 8 is equal to​

Answer 1

Answer:

Step-by-step explanation:

(1/root 9 - root 8) * (root 9 + root 8/ root 9 + root 8 )

= root 9 + root 8 / 9 - 8

= root 9 + root 8

Answer 2

Answer:

$\sf{ {\sqrt{9}} + {\sqrt{8}} }$

Step-by-step explanation:

Given : $\sf{ {\dfrac{1}{ {\sqrt{9}} - {\sqrt{8}}}}}$

Rationalising the denominator, we get

→ $\sf{ {\dfrac{1}{ {\sqrt{9}} - {\sqrt{8}} }} × {\dfrac{{\sqrt{9}} + {\sqrt{8}}}{ {\sqrt{9}} + {\sqrt{8}} }}}$

→ $\sf{ {\dfrac{(1)( {\sqrt{9}} + {\sqrt{8}})}{ ({\sqrt{9}} - {\sqrt{8}})({\sqrt{9}} + {\sqrt{8}})}}}$

Identity : (a - b)(a + b) = a² - b²

Here, a = $\sf{ {\sqrt{9}}}$ , b = $\sf{ {\sqrt{8}}}$

→ $\sf{ {\dfrac{ {\sqrt{9}} + {\sqrt{8}} }{ ({\sqrt{9}})^2 - ({\sqrt{8}})^2 }}}$

→ $\sf{ {\dfrac{ {\sqrt{9}} + {\sqrt{8}} }{ 9 - 8}}}$

→ $\sf{ {\sqrt{9}} + {\sqrt{8}} }$