Question

1) 2/√7=? 2)2/√2+1=? 3) 3-√3/2√3=? 4)a-2/√a-2√2=?

Answer 1

2/√7=2.√7/√7.√7=2√7/7

2/(√2 +1)=2.(√2-1)/(√2+1)(√2-1)=2.(√2-1)/(2-1)=2(√2-1)

(3-√3)/2√3=(3-√3)√3/2√3√3=(3√3-3)/2.3=3(√3-1)/6=(√3-1)/2

(a-2)/(√a-2√2)=(a-2)(√a+2√2)/(√a-2√2)(√a+2√2)=
=(a-2)(√a+2√2)/(a-8), a≠8

Answer 2

1) 2/√7 can be simplified by multiplying the numerator and denominator by √7 to rationalize the denominator. This gives us 2√7/7.

2) 2/√2 + 1 can be simplified by multiplying the numerator and denominator of the first fraction by √2 to rationalize the denominator. This gives us 2√2/2 + 1, which simplifies to √2 + 1.

3) (3 - √3)/2√3 can be simplified by multiplying the numerator and denominator by 2√3 to rationalize the denominator. This gives us 6√3 - 3/6, which simplifies to √3 - 1/2.

4) (a-2)/√a-2√2 can be simplified by multiplying the numerator and denominator by √a+2√2 to rationalize the denominator. This gives us (a-2)(√a+2√2)/(a-4).