Question

Simplify 7/(3-√2).
a) 3 + 2√2
b) 3 - 2√2
c) 3 + √2
d) 3 - √2

Answer 1

To simplify the expression, you need to rationalize the denominator by multiplying both the numerator and the denominator by the conjugate of the denominator.

Step-by-step explanation:

To simplify the expression 7/(3-√2), we need to rationalize the denominator by multiplying both the numerator and the denominator by the conjugate of the denominator. The conjugate of 3-√2 is 3+√2. So, the expression becomes:

7(3+√2) / ((3-√2)(3+√2))

Simplifying further, we get:

(21+7√2) / (9-2)

Finally, simplifying the expression:

(21+7√2) / 7

The simplified form of 7/(3-√2) is 3 + √2, which is option c).