💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!
Section 6
Dividing Radicals
Jonathan said that $\frac{\sqrt{10}}{2}=\sqrt{5} .$ Do you agree with Jonathan? Justify your answer.
Show that the quotient of two irrational numbers can be either rational or irrational.
In $3-29$ write each quotient in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. $$\sqrt{24} \div \sqrt{6}$$
In $3-29$ write each quotient in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. $$\sqrt{75} \div \sqrt{3}$$
In $3-29$ write each quotient in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. $$\sqrt{72} \div \sqrt{8}$$
In $3-29$ write each quotient in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. $$\sqrt{50 a^{3}} \div \sqrt{5 a}$$
In $3-29$ write each quotient in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. $$\sqrt{24 x^{2}} \div \sqrt{3 x^{3}}$$
In $3-29$ write each quotient in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. $$\frac{\sqrt{150}}{\sqrt{3}}$$
In $3-29$ write each quotient in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. $$\frac{\sqrt{54}}{\sqrt{2}}$$
In $3-29$ write each quotient in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. $$\frac{\sqrt{300}}{\sqrt{25}}$$
In $3-29$ write each quotient in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. $$\frac{\sqrt{35 a^{3}}}{\sqrt{10 a}}$$
In $3-29$ write each quotient in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. $$\frac{\sqrt{80 x^{2} y}}{\sqrt{30 x y^{2}}}$$
In $3-29$ write each quotient in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. $$\frac{\sqrt{27 b}}{\sqrt{6 b^{2}}}$$
In $3-29$ write each quotient in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. $$\frac{3}{\sqrt{3} x}$$
In $3-29$ write each quotient in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. $$\frac{7}{\sqrt{7 y}}$$
In $3-29$ write each quotient in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. $$\frac{\sqrt{12 a^{2}}}{\sqrt{4 a}}$$
In $3-29$ write each quotient in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. $$\frac{\sqrt{18 c^{3}}}{\sqrt{9 c}}$$
In $3-29$ write each quotient in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. $$\frac{4 \sqrt{2}+8 \sqrt{12}}{2 \sqrt{2}}$$
In $3-29$ write each quotient in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. $$\frac{3 \sqrt{10}-9 \sqrt{50}}{3 \sqrt{5}}$$
In $3-29$ write each quotient in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. $$\frac{\sqrt{72}+\sqrt{54}}{\sqrt{18}}$$
In $3-29$ write each quotient in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. $$\frac{\sqrt{20}-\sqrt{5}}{\sqrt{5}}$$
In $3-29$ write each quotient in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. $$\frac{\sqrt{48}+\sqrt{3}}{\sqrt{3}}$$
In $3-29$ write each quotient in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. $$\frac{\sqrt{10}+\sqrt{15}}{\sqrt{10}}$$
In $3-29$ write each quotient in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. $$\frac{5+6 \sqrt{5}}{\sqrt{5}}$$
In $3-29$ write each quotient in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. $$\frac{\sqrt[3]{27 x^{3}}+\sqrt[3]{36 x^{5}}}{\sqrt[3]{3 x^{3}}}$$
In $3-29$ write each quotient in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. $$\frac{\sqrt[4]{a b^{4}}}{\sqrt[4]{a^{2} b^{4}}}$$
In $3-29$ write each quotient in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. $$\frac{\sqrt[4]{c^{6}}}{\sqrt[5]{c^{3}}}$$
In $3-29$ write each quotient in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. $$\frac{\sqrt[3]{24 w^{2}}}{\sqrt[3]{3 w^{4}}}$$
In $3-29$ write each quotient in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. $$\frac{\sqrt{64 x^{4}}+\sqrt[4]{40 x^{6}}}{\sqrt[4]{x^{6}}}$$
The area of a rectangle is 25$\sqrt{35}$ square feet and the width is 10$\sqrt{5}$ feet. Find the length ofthe rectangle in simplest radical form.
The area of a right triangle is 6$\sqrt{2}$ square centimeters and the length of one leg is $\sqrt{12}$ cenimeters.What is the length of the other leg?What is the length of the hypotenuse?