Question

classify (5+root5)(5-root5) as rational or irrational ​

Answer 1

Answer:

It is an irrational no.

Answer 2

Given :-

• (5 + √5)(5 - √5)

To find :-

• Classify it as rational or irrational

Solution :-

Apply identity : a² - b² = (a + b)(a - b)

→ (5 + √5)(5 - √5)

→ (5)² - (√5)²

→ 25 - 5

→ 20

Hence,

• (5 + √5)(5 - √5) is rational

Extra Information

• (a + b)² = a² + b² + 2ab
• (a - b)² = a² + b² - 2ab
• (a + b)³ = a³ + b³ + 3ab(a + b)
• (a - b)³ = a³ - b³ - 3ab(a - b)