Question

Match the numbers in the first column with their respective conjugate pairs.

• A. $-\sqrt{7}$
• B. $-\sqrt{9}$
• C. $\sqrt{2}$

Answer 1

The conjugate has the same numbers but the opposite sign in the middle.

The rationalizing factor of $-\sqrt{2}$ is its conjugate pair $\sqrt{2}$.
Because while multiplying $-\sqrt{2}$ with its conjugate pair $\sqrt{2}$ will result in rational number -2
$-\sqrt{2}\times \sqrt{2}=-\sqrt{2\times 2}=-{\sqrt{\left(2\right)}}^2=-2$

The rationalizing factor of $\sqrt{7}$ is its conjugate pair $-\sqrt{7}$.
Because while multiplying $\sqrt{7}$ with its conjugate pair $-\sqrt{7}$ will result in rational number -7
$\sqrt{7}\times -\sqrt{7}=-\sqrt{7\times 7}=-{\sqrt{\left(7\right)}}^2=-7$

The rationalizing factor of $\sqrt{9}$ is its conjugate pair $-\sqrt{9}$.
Because while multiplying $\sqrt{9}$ with its conjugate pair $-\sqrt{9}$ will result in rational number -9
$\sqrt{9}\times -\sqrt{9}=-\sqrt{9\times 9}=-{\sqrt{\left(9\right)}}^2=-9$