Question

Rationalize each denominator \frac{1}{\sqrt{5}\cdot \sqrt{[)3}5}

Answer 1

To rationalize the denominator, we can multiply the numerator and denominator by the conjugate of the denominator. In this case, the conjugate is √5 - √7. After simplifying, the expression becomes √5 * √5 - √5 * √7 / 5 - √35.

Step-by-step explanation:

To rationalize the denominator, we need to eliminate the square roots from the denominator. In this case, we have the square root of 5 multiplied by the square root of 35 (which can be simplified as the square root of 5 times the square root of 7). To eliminate the square roots, we can multiply the numerator and denominator by the conjugate of the denominator. The conjugate of the denominator is the same expression but with the opposite sign in the middle (i.e., √5 - √7).

Multiplying the numerator and denominator by the conjugate, we get:

√5 * (√5 - √7) / (√5 * √5 - √5 * √7)

Expanding the denominator, we have:

√5 * (√5 - √7) / (5 - √35)

Simplifying the numerator and denominator, we get:

(√5 * √5 - √5 * √7) / (5 - √35)

The answer is:

(√5 * √5 - √5 * √7) / (5 - √35)