91Ó°ÊÓ

Add or subtract. Simplify by combining like radical terms, if possible. Assume that all variables and radicands represent positive real numbers. $$8 \sqrt{2}-\sqrt{2}+5 \sqrt{2}$$

Assume for all exercises that even roots are of non- negative quantities and that all denominators are nonzero. Write an equivalent expression using radical notation and, if possible, simplify. $$ 64^{1 / 6} $$

Express in terms of \(i\) $$ \sqrt{-12} $$

Simplify by taking the roots of the numerator and the denominator. Assume that all variables represent positive numbers. $$ \sqrt{\frac{121}{x^{2}}} $$

Solve. $$\sqrt{y+4}+6=7$$

Add or subtract. Simplify by combining like radical terms, if possible. Assume that all variables and radicands represent positive real numbers. $$\sqrt{6}-8 \sqrt{6}+2 \sqrt{6}$$

Give an exact answer and, where appropriate, an approximation to three decimal places. A right triangle's hypotenuse is \(6 \mathrm{cm}\) and one leg is \(\sqrt{5} \mathrm{cm} .\) Find the length of the other leg.

For each number, find all of its square roots. $$ 2500 $$

Assume for all exercises that even roots are of non- negative quantities and that all denominators are nonzero. Write an equivalent expression using radical notation and, if possible, simplify. $$ 9^{1 / 2} $$

Add or subtract. Simplify by combining like radical terms, if possible. Assume that all variables and radicands represent positive real numbers. $$9 \sqrt[3]{7}-\sqrt{3}+4 \sqrt[3]{7}+2 \sqrt{3}$$