Question

What needs to be done to rationalize the expression 5 over 2 minus radical 3 so there will no longer be a radical in the denominator

Answer 1

`10+5√(3)`

Explanation:

Given the expression: 5 / (2 - √3)

To rationalize the denominator, we multiply the numerator and denominator by the conjugate of the denominator. The conjugate of (2 - √3) is (2 + √3). Hence multiplying gives:

`(5)/(2-√(3) )*(2+√(3))/(2+√(3)) \\\\=(10+5√(3) )/(4+2√(3)-2√(3)-3 )\\\\Simplifying\ the\ expression:\\\\ =(10+5√(3) )/(1)\\\\= 10+5√(3)`

Hence: 5 / (2 - √3) =
`10+5√(3)`