Question

Check whether (2√3+√5) (2√3-√5) is rational or irrational

Answer 1

Answer:

Rational,of the form a^2-b^2 =12-5 =7 a rational number

Answer 2

Answer:

let √3 = x, √5 = y (to make you feel easy)

(2x + y)×(2x-y)

As (A+B)(A-B) = A² - B²,

(2x)² - (y)²

4×x² - y²

now, x² = √3² = 3.

y² = √5² = 5.

so,

4 × 3 - 5

12 - 5 = 7

As we know that 7 can be written as p/q (q≠0).

So the term (2√3 + √5)(2√3 - √5) is a rational number and is equal to 7.