Question

Simplify √(√6+2√3+√2+9/2)

Answer 1

The simplified form o
`f \( \sqrt{√(6) + 2√(3) + √(2) + (9)/(2)} \) is \( (√(2) + 3)/(√(2)) \).`

Let's simplify the expression step by step:

`\[ \sqrt{√(6) + 2√(3) + √(2) + (9)/(2)} \]`

First, combine the square root terms:

`\[ \sqrt{√(6) + √(2) + 2√(3) + (9)/(2)} \]`

Next, combine the square root and the fraction:

`\[ \sqrt{(2√(6) + √(2) + 4√(3) + 9)/(2)} \]`

Now, factor out the common factor in the numerator:

`\[ \sqrt{((√(2) + 3)^2)/(2)} \]`

Finally, simplify:

`\[ (√(2) + 3)/(√(2)) \]`

So,
`\[ \sqrt{√(6) + 2√(3) + √(2) + (9)/(2)} \]` simplifies to
`\[ (√(2) + 3)/(√(2)) \].`