Question

Rationalize the denominator:

√7-√3 /√7+√3

help me this question plZ

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Answer 1

`\tt \huge \leadsto ( √(7) - √(3) )/( √(7) + √(3) )`

`\tt \huge \leadsto ( √(7) - √(3) )/( √(7) + √(3)) * ( √(7) - √(3) )/( √(7) - √(3) )`

`\tt \huge \leadsto (7 - 3)/( (√(7 ))^(2) - ( √(3))^(2) )`

`\tt \huge \leadsto (4)/(7 - 3)`

`\tt \huge \leadsto(4)/(4)`

`\tt\huge\leadsto{1}`

Answer 2

Explanation:

To rationalize the denominator multiply the numerator and denominator by the conjugate of √7 + √3 = √7- √3

`(√(7)-√(3))/(√(7)+√(3))=((√(7)-√(3))(√(7)-√(3)))/((√(7)+√(3))(√(7)-√(3)))\\\\\\= ((√(7)-√(3))^(2))/((√(7))^(2)-(√(3))^(2))\\\\\\= ((√(7))^(2)-2*(√(7))*(√(3))+(√(3))^(2)))/(7-3)\\\\=(7-2√(21)+3)/(4)\\\\=(10-2√(21))/(4)\\\\=(2(5-√(21)))/(4)\\\\=(5-√(21))/(2)`