How do you simplify $\frac{9}{6 - \sqrt{8}}$ $9/(6-sqrt8)$ ?

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Answer 1 · 2017-07-19T04:59:25

Multiply the top and bottom by $(6 + \sqrt{8})$ $(6 + sqrt8)$ to make a difference of two squares and remove the square root.

The difference of two squares:
$(a + b) (a - b) = a^{2} - a b + a b - b^{2} = a^{2} - b^{2}$ $(a + b)(a -b) = a^2 - ab + ab -b^2 = a^2 - b^2$

$= \frac{9 (6 + \sqrt{8})}{(6 - \sqrt{8}) (6 + \sqrt{8})}$ $= (9(6+sqrt8))/((6-sqrt8)(6+sqrt8))$

$= \frac{54 + 9 \sqrt{8}}{6^{2} - {(\sqrt{8})}^{2}}$ $=(54+9sqrt8)/(6^2 - (sqrt8)^2)$

$= \frac{54 + 9 \sqrt{8}}{36 - 8}$ $=(54+9sqrt8)/(36-8)$

$= \frac{54 + 9 \sqrt{8}}{28}$ $=(54+9sqrt8)/28$

This is now simplified, as a fraction can have a root on top, but not on the bottom (as then it is irrational).

You could also round this value to 2.84, but the answer calculated is exact.

How do you simplify 96−√89/(6-sqrt8)?