Question

Simplify each of the following expressions :
I) (3+√3) (2+√2)
II) (3+√3) (3-√3)
III) (√5+√2)²
IV) (√5-√2) (√5+√2)​

Answer 1

Answer:

1) 6+ ✓6+ 2✓3+ 3✓2

2) 6

3) 7+2✓10

4)3

Answer 2

Answer:

(I) 6+3√2+2√3+√6

(II) 6

(III) 7+2√10

(IV) 3

Step-by-step explanation:

(I) (3+√3)(2+√2)

6+3√2+2√3+√6

(II) (3+√3)(3-√3)

Using identities,

(a+b)(a-b)=a²-b²

(3)²-(√3)²

9-3

6

(III) (√5+√2)²

Using identities,

(a+b)²=a²+b²+2ab

(√5)²+(√2)²+2(√5)(√2)

5+2+2√10

7+2√10

(IV) (√5-√2)(√5+√2)

Using identities,

(a-b)(a+b)=a²-b²

(√5)²-(√2)²

5-2

3