Question

Rationalize denominator 7-3√2/7+3√2

Answer 1

$Hey\: there!\\ \\ Solution:\\ \\ \frac{7 - 3\sqrt{2}}{7 + 3\sqrt{2}} × \frac{7 - 3\sqrt{2}}{7 - 3\sqrt{2}}\\ \\ Using\: Identities:\\ \\ ( a + b ).( a - b ) = a^{2} - b^{2} \\ \\ ( a - b ).( a - b ) = ( a - b )^{2}\\ \\ =\frac{(7 - 3\sqrt{2})^{2}}{(7)^{2} - (3\sqrt{2})^{2}}\\ \\ Again \:Using\: Identity: ( a - b )^{2} = a^{2} + b^{2} - 2ab\\ \\ =\frac{ (7)^{2} + (3\sqrt{2})^{2} - ( 2 )( 7 ) 3\sqrt{2}}{49 - 9 × 2}\\ \\ =\frac{49 + 9 × 2 - 42\sqrt{2}}{49 - 18}\\ \\ = \frac{49 + 18 - 42\sqrt{2}}{31}\\ \\= \frac{67 - 42\sqrt{2}}{31}$



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Answer 2

Question about
Rationalizing the denominator

7-3√2/7+3√2
Multiply the numerator and denominator by 7-3√2

=(7-3√2)/(7+3√2)×(7-3√2)/(7-3√2)

write the repeated multiplication in exponential form.

(7-3√2)²/49-9×2

using(a-b)²=a²-2ab+b² expand the expressions

49-42√2+18/49-18
Add the numbers.
67-42√2/49-18
=67-42√2/31