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Section 3
Simplifying Radicals
Explain the difference between $-\sqrt{36}$ and $\sqrt{-36}$
If $a$ is a negative number, is $-\sqrt[3]{-8 a^{3}}$ a positive number, a negative number, or not a realnumber? Explain your answer. oning Skills.
In $3-38$ , write each radical in simplest radical form. Variables in the radicand of an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero.$$\sqrt{12}$$
In $3-38$ , write each radical in simplest radical form. Variables in the radicand of an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero.$$\sqrt{50}$$
In $3-38$ , write each radical in simplest radical form. Variables in the radicand of an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero.$$\sqrt{32}$$
In $3-38$ , write each radical in simplest radical form. Variables in the radicand of an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero.$$\sqrt[4]{48 a^{9} b^{3}}$$
In $3-38$ , write each radical in simplest radical form. Variables in the radicand of an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero.$$\sqrt{8 b^{3}}$$
In $3-38$ , write each radical in simplest radical form. Variables in the radicand of an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero.$$\sqrt{98 c^{4}}$$
In $3-38$ , write each radical in simplest radical form. Variables in the radicand of an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero.$$5 \sqrt{200 x y^{2}}$$
In $3-38$ , write each radical in simplest radical form. Variables in the radicand of an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero.$$3 \sqrt{20 y^{5}}$$
In $3-38$ , write each radical in simplest radical form. Variables in the radicand of an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero.$$\sqrt[3]{16}$$
In $3-38$ , write each radical in simplest radical form. Variables in the radicand of an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero.$$4 \sqrt{363 x^{5} y^{7}}$$
In $3-38$ , write each radical in simplest radical form. Variables in the radicand of an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero.$$\sqrt[3]{24}$$
In $3-38$ , write each radical in simplest radical form. Variables in the radicand of an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero.$$\cdot \frac{1}{2} \sqrt{7} 2 a b^{5}$$
In $3-38$ , write each radical in simplest radical form. Variables in the radicand of an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero.$$\sqrt[3]{40 a^{4}}$$
In $3-38$ , write each radical in simplest radical form. Variables in the radicand of an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero.$$\sqrt{\frac{3 x}{4 y}}$$
In $3-38$ , write each radical in simplest radical form. Variables in the radicand of an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero.$$\sqrt{\frac{4 a^{4}}{25}}$$
In $3-38$ , write each radical in simplest radical form. Variables in the radicand of an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero.$$\sqrt{\frac{3 b^{3}}{44}}$$
In $3-38$ , write each radical in simplest radical form. Variables in the radicand of an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero.$$\sqrt{\frac{6}{81 y^{6}}}$$
In $3-38$ , write each radical in simplest radical form. Variables in the radicand of an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero.$$\sqrt{\frac{a^{5}}{2}}$$
In $3-38$ , write each radical in simplest radical form. Variables in the radicand of an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero.$$\cdot \sqrt{\frac{a^{3}}{5 b}}$$
In $3-38$ , write each radical in simplest radical form. Variables in the radicand of an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero.$$\sqrt{\frac{1}{6 x y}}$$
In $3-38$ , write each radical in simplest radical form. Variables in the radicand of an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero.$$\sqrt{\frac{3}{5 b^{5}}}$$
In $3-38$ , write each radical in simplest radical form. Variables in the radicand of an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero.$$\sqrt{\frac{5 a}{18}}$$
In $3-38$ , write each radical in simplest radical form. Variables in the radicand of an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero.$$\sqrt{\frac{15}{8 b^{3}}}$$
In $3-38$ , write each radical in simplest radical form. Variables in the radicand of an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero.$$\sqrt{\frac{4 a^{3}}{27 b^{3}}}$$
In $3-38$ , write each radical in simplest radical form. Variables in the radicand of an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero.$$\sqrt{\frac{9}{50 x y^{7}}}$$
In $3-38$ , write each radical in simplest radical form. Variables in the radicand of an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero.$$\sqrt{\frac{8 x}{5 y^{3}}}$$
In $3-38$ , write each radical in simplest radical form. Variables in the radicand of an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero.$$\sqrt{0.08}$$
In $3-38$ , write each radical in simplest radical form. Variables in the radicand of an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero.$$\sqrt{0.5}$$
In $3-38$ , write each radical in simplest radical form. Variables in the radicand of an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero.$$\sqrt{2.42 a b^{5}}$$
In $3-38$ , write each radical in simplest radical form. Variables in the radicand of an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero.$$\sqrt{0.001 x^{3}}$$
In $3-38$ , write each radical in simplest radical form. Variables in the radicand of an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero.$$\sqrt{128 x^{2}}$$
In $3-38$ , write each radical in simplest radical form. Variables in the radicand of an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero.$$\sqrt{300 c}$$
In $3-38$ , write each radical in simplest radical form. Variables in the radicand of an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero.$$\sqrt[3]{\frac{a^{3}}{3}}$$
In $3-38$ , write each radical in simplest radical form. Variables in the radicand of an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero.$$\sqrt[4]{\frac{2 a^{8}}{b^{2} c^{3}}}$$
In $3-38$ , write each radical in simplest radical form. Variables in the radicand of an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero.$$\sqrt[4]{32 x^{5} y^{4}}$$
The lengths of the legs of a right triangle are 8 centimeters and 12 centimeters. Express the length of the hypotenuse in simplest radical form.
The length of one leg of an isosceles right triangle is 6 inches. Express the length of the hypotenuse in simplest radical form.
The length of the hypotenuse of a right triangle is 24 meters and the length of one leg is 12 meters. Express the length of the other leg in simplest radical form.
The dimensions of a rectangle are 15 feet by 10 feet. Express the length of the diagonal in simplest radical form.
The area of a square is 150 square feet. Express the length of a side of the square in simplest radical form.
The area of a circular pool is 5$x^{2} y^{4} \pi$ square meters. Express the radius of the pool in sim-plest radical form.
The area of a triangle is $\sqrt[5]{243 x^{5} y^{10}}$ square units. If the length of a side of the triangle is $\sqrt[5]{x^{5}}$ express the length of the altitude to that side in simplest radical form. (1) A walking stick 42 inches long(2) A fishing rod 37 inches long(3) A yardstick(4) A baseball bat 34 inches long