Question

Simplify 3/√7 - √2.

A) √7 - 2√2
B) √7 - √2
C) √7 + √2
D) √7 - √14

Answer 1

The simplified form of 3/√7 - √2 is √7 - √14. So, option D is correct.

Step-by-step explanation:

To simplify the expression 3/√7 - √2, let's rationalize the denominator of the first term. Multiply both the numerator and denominator of the fraction by the conjugate of the denominator:

`\[ (3)/(√(7)) \cdot (√(7))/(√(7)) = (3√(7))/(7) \]`

Now, the expression becomes
`\( (3√(7))/(7) - √(2) \)`. To combine the terms, find a common denominator, which is 7:

`\[ (3√(7))/(7) - (7√(2))/(7) = (3√(7) - 7√(2))/(7) \]`

Now, you can factor out the common factor of √7 from the numerator:

`\[ (√(7)(3 - 7√(2)/√(7)))/(7) \]`

Simplify further:

`\[ (√(7)(3√(7) - 7√(2)))/(7) \]`

Finally, cancel out the common factor of √7:

`\[ 3 - 7√(2) \]`

So, the simplified expression is
`\( √(7) - √(14) \)`, which corresponds to option D.