Question

(5+root 7)+(7+5×root 3) pls give step by step explanation and don't give ans in decimal

Answer 1

The first question that pops up in mind, what is a rational number or irrational number :

• Rational numbers: The numbers which can be expressed in the form of a/b, where both a and b are integers with b ≠ 0. E.g., 0, 1, 5/7, ... .
• Irrational numbers: The numbers which cannot be expressed in the form of a fraction, are called irrational numbers. E.g., √3, √5, 2 + √3, ... .

Now we solve the given problem :

Now, (5 + √7) (7 + 5√3)

= 5 (7 + 5√3) + √7 (7 + 5√3)

= 5 (7) + 5 (5√3) + √7 (7) + √7 (5√3)

= 35 + 25√3 + 7√7 + 5√21

∴ (5 + √7) (7 + 5√3) = 35 + 25√3 + 7√7 + 5√21