Question

5. Simplify each of the following expressions:
(i) (√3+1) (√3-1)
(ii) (√5+2)(√3-1)
(iii) (√7+1)2

Answer 1

ANSWER:

1. (2)
2. -2+√15-√5+2√3
3. 2√7+2

GIVEN:

(i) (√3+1) (√3-1)

(ii) (√5+2)(√3-1)

(iii) (√7+1)2

TO FIND:

• Value of above expressions.

SOLUTION:

(i)

= (√3+1)(√3-1)

= (√3)²-(1)²

= 3-1

= 2

(ii)

= (√5+2)(√3-1)

= √5(√3-1)+2(√3-1)

= √15-√5+2√3-2

= -2+√15-√5+2√3

(iii)

= (√7+1)2

= 2√7+2

Or the third question ask about finding the square of (√7+1) then:

= (√7+1)²

= (√7)²+(1)²+2√7*1

= 7+1+2√7

= 8+2√7

NOTE:

Some important formulas:

• (a+b)(a-b) = a²-b²
• (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)