Question

simplify of the following expression (√5-√2)(√5+√2)​

Answer 1

Answer:

(5+2)(5−2)

We know that (a+b)(a−b)=a2−b2

=(5+2)(5−2)

=(5)2−(2)2

=5−2

=3

Answer 2

Given Equation → (√5 - √2) (√5 + √2)

Here we apply the formula of (a + b)(a - b) = a² - b²

Applying this formula,

(√5 - √2) (√5 + √2)

⇒ (√5)² - (√2)²

Cancelling square and square root,

⇒ 5 - 2

⇒ 3

So, (√5 - √2) (√5 + √2) = 3

SOME USEFUL IDENTITIES:

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