Simplify the expression. (10)/(√(2)+√(7) )

Question

Simplify the expression.


`(10)/(√(2)+√(7) )`

Answer 1

Explanation:

`(10)/(√(2)+√(7))=(10*(√(2)-√(7)))/((√(2)+√(7))*(√(2)-√(7)))\\\\=(10*(√(2)-√(7)))/((√(2))^(2)-(√(7))^(2))\\\\=(10*(√(2)-√(7)))/(2-7)\\\\=(10*(√(2)-√(7)))/(-5)\\\\=-2*(√(2)-√(7))\\\\= -2√(2)+2√(7)`

Hint: (a + b)(a -b)= a² - b²

(√2+√7)(√2-√7)=(√2)²-(√7²) = 2 - 7 = -5