Tính: √12/√5 – √3

1. To simplify √12/√5 – √3, we can start by rationalizing the denominator of the first term.

√12/√5 can be written as (√12/√5) * (√5/√5) = √60/5.

So, the expression becomes √60/5 – √3.

To simplify further, we can factor the square root of 60.

√60 = √(4 * 15) = √4 * √15 = 2√15.

Therefore, the expression becomes 2√15/5 – √3.

2. To simplify 2 + √3/2 – √3, we can start by rationalizing the denominator of the second term.

√3/2 can be written as (√3/2) * (√2/√2) = √6/2.

So, the expression becomes 2 + √6/2 – √3.

To simplify further, we can multiply the whole expression by 2/2 to get rid of the fraction.

(2 * 2 + √6)/2 – √3 = (4 + √6)/2 – √3.

3. To simplify √2 + 1/√2 – 1, we can start by rationalizing the denominator of the second term.

1/√2 can be written as (1/√2) * (√2/√2) = √2/2.

So, the expression becomes √2 + √2/2 – 1.

To simplify further, we can combine the terms with the same denominator.

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

4. To simplify 3√2/√3 + 1, we can start by rationalizing the denominator of the first term.

√3 can be written as (√3) * (√3/√3) = 3/√3.

So, the expression becomes 3√2/(3/√3) + 1.

To simplify further, we can multiply the numerator and denominator of the first term by √3.

(3√2 * √3)/(3 * √3) + 1 = (3√6)/3 + 1.

Simplifying further, we can cancel out the 3's in the numerator and denominator.

√6 + 1.