Question

A. Determine whether the statement is true or false. Write \( T \) if it is true and \( F \) if otherwise. \( \qquad \) 1. Rationalizing the denominator of a radical number always results in a whole number. \( \qquad \) 2. In the expression \( \sqrt[n]{b^{m}} \), the simplest form becomes nonnegative when \( m=n \). \( \qquad \) 3. The expression \( \sqrt[n]{b^{m}} \) has two real roots for every value of \( n \) and \( b \). \( \qquad \) 4. The expression \( \sqrt[6]{b^{3}} \) is in its simplest form. \( \qquad \) 5. The expression \( \sqrt[4]{\sqrt[2]{81}} \) is equivalent to \( \sqrt[4]{3} \). B. Simplify the radical expression. 1. \( \sqrt{50} \) 9. \( \sqrt[3]{\left(-3 b^{2} y^{6}\right)^{3}} \) 2. \( \sqrt{-147} \) 10. \( \sqrt{200 m^{8} n^{4}} \) 3. \( \sqrt[3]{32} \) 11. \( -2 \sqrt{25 x-25 y} \) 4. \( 4 \cdot \sqrt[8]{4^{8}} \) 12. \( \frac{\sqrt[3]{-16 a^{10}}}{\sqrt[3]{54 a^{7}}} \) 5. \( \sqrt[4]{243} \) 13. \( \sqrt{\frac{36}{121 x^{2}}} \) 6. \( \sqrt[4]{(a-6)^{4}} \) 14. \( \sqrt{\sqrt[3]{a^{12} b^{18} c^{-6}}} \) 7. \( \sqrt[3]{81 a^{5} b^{7} c^{2}} \) 15. \( \sqrt[3]{-n^{6} \sqrt{4^{3} m^{2} n^{4}}} \) 8. \( \sqrt[5]{25^{2 x+1}, 5^{x+5}} \)

          A. Determine whether the statement is true or false. Write \( T \) if it is true and \( F \) if otherwise.
\( \qquad \) 1. Rationalizing the denominator of a radical number always results in a whole number.
\( \qquad \) 2. In the expression \( \sqrt[n]{b^{m}} \), the simplest form becomes nonnegative when \( m=n \).
\( \qquad \) 3. The expression \( \sqrt[n]{b^{m}} \) has two real roots for every value of \( n \) and \( b \).
\( \qquad \) 4. The expression \( \sqrt[6]{b^{3}} \) is in its simplest form.
\( \qquad \) 5. The expression \( \sqrt[4]{\sqrt[2]{81}} \) is equivalent to \( \sqrt[4]{3} \).
B. Simplify the radical expression.
1. \( \sqrt{50} \)
9. \( \sqrt[3]{\left(-3 b^{2} y^{6}\right)^{3}} \)
2. \( \sqrt{-147} \)
10. \( \sqrt{200 m^{8} n^{4}} \)
3. \( \sqrt[3]{32} \)
11. \( -2 \sqrt{25 x-25 y} \)
4. \( 4 \cdot \sqrt[8]{4^{8}} \)
12. \( \frac{\sqrt[3]{-16 a^{10}}}{\sqrt[3]{54 a^{7}}} \)
5. \( \sqrt[4]{243} \)
13. \( \sqrt{\frac{36}{121 x^{2}}} \)
6. \( \sqrt[4]{(a-6)^{4}} \)
14. \( \sqrt{\sqrt[3]{a^{12} b^{18} c^{-6}}} \)
7. \( \sqrt[3]{81 a^{5} b^{7} c^{2}} \)
15. \( \sqrt[3]{-n^{6} \sqrt{4^{3} m^{2} n^{4}}} \)
8. \( \sqrt[5]{25^{2 x+1}, 5^{x+5}} \)

A. Determine whether the statement is true or false. Write T if it is true and F if otherwise.
1. Rationalizing the denominator of a radical number always results in a whole number.
2. In the expression √(b^m), the simplest form becomes nonnegative when m=n.
3. The expression √(b^m) has two real roots for every value of n and b.
4. The expression √(b^3) is in its simplest form.
5. The expression √(√(81)) is equivalent to √(3).
B. Simplify the radical expression.
1. √(50)
9. √((-3 b^2 y^6)^3)
2. √(-147)
10. √(200 m^8 n^4)
3. √(32)
11. -2 √(25 x-25 y)
4. 4 ·√(4^8)
12. (√(-16 a^10))/(√(54 a^7))
5. √(243)
13. √((36)/(121 x^2))
6. √((a-6)^4)
14. √(√(a^12 b^18 c^-6))
7. √(81 a^5 b^7 c^2)
15. √(-n^6√(4^3 m^2 n^4))
8. √(25^2 x+1, 5^x+5)

Added by Gregg M.

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