Question

Rationalize 2 divided by square root of 2 pluse square root of 3 plus 1

Answer 1

To rationalize
`\( (2)/(√(2) + √(3) + 1) \)`, multiply both the numerator and denominator by the conjugate
`\((√(2) - √(3) - 1)\)`. The simplified result is
`\(2√(2) - 2√(3) - 2\)`.

To rationalize the given expression, multiply the numerator and denominator by the conjugate of the denominator. The conjugate is obtained by changing the sign between the terms with square roots. In this case, the conjugate of the denominator is
`\((√(2) - √(3) - 1)\)`:

`\[(2)/(√(2) + √(3) + 1) * (√(2) - √(3) - 1)/(√(2) - √(3) - 1)\]`

Now, multiply the numerators and denominators:

`\[(2(√(2) - √(3) - 1))/((√(2) + √(3) + 1)(√(2) - √(3) - 1))\]`

Simplify the denominator by applying the difference of squares:

`\[(√(2) + √(3) + 1)(√(2) - √(3) - 1) = 2 - 1 = 1\]`

Therefore, the expression simplifies to:

`\[2(√(2) - √(3) - 1)\]`

So, the rationalized form is
`\(2√(2) - 2√(3) - 2\)`.