Question

Write the expression in simplest form. 5/3-√2=

Answer 1

`(15+5√(2))/(7)`

Explanation:

Given rational expression:

`(5)/(3-√(2))`

To write the given rational expression in its simplest form we need to rationalise the denominator by multiplying both the numerator and denominator by the conjugate of the denominator.

The conjugate of an expression is where we change the sign in the middle of the two terms. Therefore, the conjugate of the denominator of the given expression is:

• 
  `3+√(2)`

Multiply the numerator and denominator by the conjugate of the denominator:

`(5)/(3-√(2)) \cdot (3+√(2))/(3+√(2))`

Simplify:

`\implies (5(3+√(2)))/((3-√(2))(3+√(2)))`

`\implies (15+5√(2))/(9+3√(2)-3√(2)-2)`

`\implies (15+5√(2))/(9-2)`

`\implies (15+5√(2))/(7)`

Answer 2

`\sf \: (5 - 3 √(2) )/(3)`

Explanation:

Given expression,

→ (5/3) - √2

Let's simplify the expression,

→ (5/3) - √2

→ (5/3) - ((√2 × 3)/(1 × 3))

→ (5/3) - (3√2/3)

→ (5 - 3√2)/3

Hence, answer is (5 - 3√2)/3.