Question

What is the simplest form of the radical expression the square root of 2 + the square root of 5 divided by the square root of 2 - the square root of 5

Answer 1

1/-3 (7+2√10) is the simplification of given expression.

Explanation:

We have given the expression:

√2+√5 /√2-√5

We have to find the simplest form of the given expression.

For simplification of this expression we have to multiply and divide the expression by (√2+√5).

(√2+√5)/(√2-√5) ×(√2 +√5)/(√2+√5)

(√2+√5)²/(√2)² - (√5)²

(√2+√5)²/ (2-5)

(√2)²+(√5)²+ 2(√2)(√5) / -3

2+5+2√10 /-3

(7+2√10) / -3

1/-3 (7+2√10) is the simplification of given expression.

Answer 2

For this case, we have the following expression:

`\frac {\sqrt {2} + \sqrt {5}} {\sqrt {2} - \sqrt {5}}`

We must rationalize, that is, we multiply the numerator and denominator by
`\sqrt {2} + \sqrt {5}`:

`\frac {(\sqrt {2} + \sqrt {5}) * (\sqrt {2} + \sqrt {5})} {(\sqrt {2} - \sqrt {5}) * (\sqrt { 2} + \sqrt {5})} =\\\frac {(\sqrt {2} + \sqrt {5}) ^ 2} {(\sqrt {2} - \sqrt {5}) (\sqrt {2} + \sqrt {5})} =\\\frac {(\sqrt {2} + \sqrt {5}) ^ 2} {(\sqrt {2}) ^ 2+ √(2) \sqrt {5} - \sqrt {5} \sqrt {2} - (\sqrt {5}) ^ 2} =`

`\frac {(\sqrt {2} + \sqrt {5}) ^ 2} {2-5} =\\\frac {(\sqrt {2} + \sqrt {5}) ^ 2} {- 3} =\\\frac {(\sqrt {2}) ^ 2 + 2 \sqrt {2} \sqrt {5} + (\sqrt {5}) ^ 2} {- 3} =\\\frac {2 + 2 \sqrt {10} +5} {- 3} =`

`- \frac {1} {3} (7 + 2 \sqrt {10})`

ANswer:

`- \frac {1} {3} (7 + 2 \sqrt {10})`