Answer:
1. √6/2
2. (√35-3√7)/2
3. 6√5+√10
4. 3^√22
Explanation:
1. Simplify 6/( square root of 2). 6√2 6 2. Step 1. Multiply 6√2 6 2 by √2√2 2 2 . 6√2⋅√2√2 6 2 ⋅ 2 2. Step 2. Combine and simplify the denominator.
2. To simplify √7/√5+3, we need to rationalize the denominator by multiplying both the numerator and denominator by √5-3. This gives us (√7)(√5-3)/(√5+3)(√5-3), which simplifies to (√35-3√7)/2.
3. We can simplify √5(6+√2) by distributing the √5, which gives us 6√5+√10.
4. 3^√6•3^√16 can be simplified by using the rule that a^b • a^c = a^(b+c). This gives us 3^√22.