91Ó°ÊÓ

Find each square root. If it is not exact, give a decimal approximation correct to three decimal places. $$\sqrt{\frac{196}{225}}$$

Simplify. Assume that all variables in the radicand of an even root represent positive values. Assume no division by 0. Express each answer with positive exponents only. $$(-125)^{1 / 3}$$

Simplify. All variables in square root problems represent positive values. Assume no division by 0. $$\sqrt{y}(\sqrt{y}+5)$$

Simplify. All variables represent positive values. $$\sqrt{1,000}-\sqrt{360}$$

Simplify each expression. All variables of square root expressions represent positive numbers. Assume no division by 0. $$\sqrt{432}$$

Simplify. Assume that all variables in the radicand of an even root represent positive values. Assume no division by 0. Express each answer with positive exponents only. $$16^{1 / 4}$$

Simplify. All variables in square root problems represent positive values. Assume no division by 0. $$7 \sqrt[3]{3 x}(2+\sqrt[3]{9 x^{2}})$$

Use a calculator to help solve each. Give any decimal answer rounded to the nearest tenth. Einstein's theory of relativity predicts that a clock moving at speed \(v\) will run slower by a factor \(f\) given by $$f=\frac{1}{\sqrt{1-\frac{v^{2}}{c^{2}}}}$$ where \(c\) is the speed of light. Solve this equation for \(v^{2}\)

Simplify. Assume that all variables in the radicand of an even root represent positive values. Assume no division by 0. Express each answer with positive exponents only. $$81^{1 / 4}$$

Simplify each expression. All variables of square root expressions represent positive numbers. Assume no division by 0. $$\sqrt{720}$$