Use long division to solve 3√63

We look for factors of 63 that are perfect squares.

$$63 = 9 \times 7$$

Since 9 is a perfect square ($3^2$), we can rewrite $\sqrt{63}$ as:

$$\sqrt{63} = \sqrt{9 \times 7}$$ $$\sqrt{63} = \sqrt{9} \times \sqrt{7}$$ $$\sqrt{63} = 3\sqrt{7}$$

Now, substitute $3\sqrt{7}$ for $\sqrt{63}$ in the original expression $3\sqrt{63}$:

$$3 \times (3\sqrt{7})$$ $$3 \times 3 \times \sqrt{7}$$ $$9\sqrt{7}$$

If a numerical answer is required, we can approximate $\sqrt{7}$:

$$\sqrt{7} \approx 2.64575$$

Then multiply by 9:

$$9 \times 2.64575 \approx 23.81175$$

The simplified exact form is $9\sqrt{7}$. The approximate value is 23.81175.

$$9\sqrt{7} \approx 23.81175$$