Question

Multiply and combine like terms. Then explain what you notice about the two different results. (i) (√3+√2)(√3+√2) (ii) (√3+√2)(√3-√2)

Answer 1

(i) 5 + 2√6

(ii) 1 - 2√6

Explanation:

(i) (√3+√2)(√3+√2)

⇒ √3(√3+√2) + √2(√3+√2)

or

⇒ (√3)² + (√3 × √2) + ( √2 ×√3 ) + ( √2 × √2 )

or

⇒ 3 + √6 + √6 + 2

or

⇒ 5 + 2√6

(ii) (√3+√2)(√3-√2)

⇒ √3(√3-√2) + √2(√3-√2)

or

⇒ ( √3 × √3 ) - ( √3 × √2) + ( √2 × √3 ) - ( √2 ×√2)

or

⇒ ( 3 ) - ( √6 ) + ( √6 ) - ( 2 )

or

⇒ 1 - 2√6