91Ó°ÊÓ

In each of the following, perform the indicated operations and simplify as completely as possible. Assume all variables appearing under radical signs are non negative. $$\sqrt{24}+\frac{5}{\sqrt{6}}$$

Estimate the given square root between two consecutive integers without using a calculator, then use a calculator to find the square root rounded to two decimal places to confirm your estimate. $$\sqrt{673}$$

The period of a pendulum is the time it takes for the pendulum to sweep out one complete arc. The formula (in seconds) for the period \(T\) of a pendulum of length \(L\) feet is $$ T=2 \pi \sqrt{\frac{L}{32}} $$ Find the length of a pendulum with a period of 2 seconds.

Perform the indicated operations. Simplify all answers as completely as possible. Assume that all variables appearing under radical signs are nonnegative. $$\frac{\sqrt{3}}{2+\sqrt{3}}$$

Simplify each expression as completely as possible. Be sure your answers are in simplest radical form. Assume that all variables appearing under radical signs are nonnegative. $$\frac{\sqrt{8}}{\sqrt{6}}$$

In each of the following, perform the indicated operations and simplify as completely as possible. Assume all variables appearing under radical signs are non negative. $$\frac{\sqrt{8}}{7}+\frac{7}{\sqrt{2}}$$

In each of the following, perform the indicated operations and simplify as completely as possible. Assume all variables appearing under radical signs are non negative. $$\frac{\sqrt{12}}{5}+\frac{5}{\sqrt{3}}$$

Perform the indicated operations. Simplify all answers as completely as possible. Assume that all variables appearing under radical signs are nonnegative. $$\frac{\sqrt{5}}{\sqrt{6}-\sqrt{5}}$$

Estimate the given square root between two consecutive integers without using a calculator, then use a calculator to find the square root rounded to two decimal places to confirm your estimate. $$\sqrt{318}$$

Simplify each expression as completely as possible. Be sure your answers are in simplest radical form. Assume that all variables appearing under radical signs are nonnegative. $$\frac{\sqrt{12}}{\sqrt{18}}$$