Answer:
1. x = 81
2. x = 72
3. x = 9/4
4. x = 25
5. x = E∅
6. x = 49/3
7. x = 32
8. x = 189
9. x = 1
10. x = 64
Solution:
[tex]1. \sqrt{x} = 9 \\ \ \\ x = 81[/tex]
[tex]2. \: \sqrt[3]{3x} = 6 \\ \\ 3x = 216 \\ x = 72[/tex]
[tex]3. \: 4 \sqrt{x} = 6 \\ 2 \sqrt{x} = 3 \\ 4 = 9 \\ x = \frac{4}{9} \\ 4 \sqrt{ \frac{9}{4} } = 6 \\ 6 = 6 \\ x = \frac{9}{4} [/tex]
[tex]4. \: 7 + \sqrt{ \times } = 12 \\ \sqrt{x} = 12 - 7 \\ \sqrt{x} = 5 \\ x = 25 \\ 7 + \sqrt{25} = 12 \\ 12 = 12 \\ x = 25[/tex]
[tex]4. \: 7 + \sqrt{ \times } = 12 \\ \sqrt{x} = 12 - 7 \\ \sqrt{x} = 5 \\ x = 25 \\ 7 + \sqrt{25} = 12 \\ 12 = 12 \\ x = 25[/tex]
[tex]5. \: \sqrt[4]{3x} - 5 = - 8 \\ \sqrt[4]{3x} - 8 + 5 \\ \sqrt[4]{3x} = - 3 \\ [/tex]
x = E∅
The statement is false for any value of x because the even root function is always positive or 0.
[tex]6. \: \sqrt{3x - 2} = 5 \\ \sqrt{3x} = 5 + 2 \\ \sqrt{3x} = 7 \\ 3x = 79 \\ x \frac{49}{3} - 2 = 5 \\ 5 = 5 \\ x = \frac{49}{3} [/tex]
[tex]7. \: \sqrt[5]{x} + 5 = 7 \\ \sqrt[5]{x} = 7 - 5 \\ \sqrt[5]{x} = 2 \\ x = 32[/tex]
[tex]8. \: \sqrt[3]{x} = 3 \sqrt[3]{7} \\ x = 27 \: \times 7 \\ x = 189[/tex]
[tex]9. \: 8 - \sqrt[4]{x} = 7 \\ - \sqrt[ 4]{x} = 7 - 8 \\ - \sqrt[4]{x} = 1 \\ \sqrt[4]{x} = 1 \\ 8 - \sqrt[4]{1} = 7 \\ 7 = 7 \\ x = 1[/tex]
[tex]10. \: \: 3 \sqrt[3]{x} = 12 \\ \sqrt[3]{x} = 12 \\ \sqrt[3]{x } = 4 \\ x = 64[/tex]
