Name
8-3 Additional Practice
Solving Quadratic Equations Using Square Roots
Solve each equation by inspection.
1. \( x^{2}=64 \)
2. \( x^{2}=-169 \)
3. \( x^{2}=108 \)
4. \( x^{2}=200 \)
Solve each equation.
5. \( 4 x^{2}=81 \)
6. \( -3 x^{2}=-54 \)
7. \( -7 x^{2}=49 \)
8. \( \frac{1}{5} x^{2}=80 \)
9. \( 2 x^{2}-3=11 \)
10. \( -3 x^{2}+4=-104 \)
11. \( \frac{1}{2} x^{2}-3=37 \)
12. \( 3 x^{2}+5=-145 \)
13. How can you solve \( a x^{2}=c \) and \( a x^{2}+b=c \) ? Assume \( a \neq c \). What is the solution to each equation?
14. The formula for the volume of a cylinder is \( V=\pi r^{2} h \). What is the radius for a cylinder that has a volume of \( 160 \pi \mathrm{m}^{3} \) and a height of \( 8 \mathrm{~m} \) ? Express your answer in simplest radical form and as a decimal rounded to the nearest tenth.
enVision \( { }^{\circledast} \) Florida B.E.S.T. Algebra 1 • Teaching Resources

Step 1 ：\( x_{1} = \sqrt{64} \), \( x_{2} = -\sqrt{64} \)

Step 2 ：No real solution

Step 3 ：\( x_{1} = \sqrt{108} \), \( x_{2} = -\sqrt{108} \)

Step 4 ：\( x_{1} = \sqrt{200} \), \( x_{2} = -\sqrt{200} \)

Step 5 ：\( \frac{4 x^{2}}{4} = \frac{81}{4} \), \( x_{1} = \sqrt{\frac{81}{4}} \), \( x_{2} = -\sqrt{\frac{81}{4}} \)

Step 6 ：\( \frac{-3 x^{2}}{-3} = \frac{-54}{-3} \), \( x_{1} = \sqrt{18} \), \( x_{2} = -\sqrt{18} \)

Step 7 ：\( \frac{-7 x^{2}}{-7} = \frac{49}{-7} \), \( x_{1} = \sqrt{7} \), \( x_{2} = -\sqrt{7} \)

Step 8 ：\( 5 x^{2} = 400 \), \( x_{1} = \sqrt{80} \), \( x_{2} = -\sqrt{80} \)

Step 9 ：\( 2 x^{2} = 14 \), \( \frac{2 x^{2}}{2} = \frac{14}{2} \), \( x_{1} = \sqrt{7} \), \( x_{2} = -\sqrt{7} \)

Step 10 ：\( -3 x^{2} = -100 \), \( \frac{-3 x^{2}}{-3} = \frac{-100}{-3} \), \( x_{1} = \sqrt{\frac{100}{3}} \), \( x_{2} = -\sqrt{\frac{100}{3}} \)

Step 11 ：\( \frac{1}{2} x^{2} = 40 \), \( x_{1} = \sqrt{80} \), \( x_{2} = -\sqrt{80} \)

Step 12 ：\( 3 x^{2} = -150 \), \( \frac{3 x^{2}}{3} = \frac{-150}{3} \), \( x_{1} = \sqrt{50}i \), \( x_{2} = -\sqrt{50}i \)

Step 13 ：For \( a x^{2}=c \), \( x_{1} = \sqrt{\frac{c}{a}} \), \( x_{2} = -\sqrt{\frac{c}{a}} \); For \( a x^{2}+b=c \), first isolate \( a x^{2} \) by subtracting \( b \) from both sides, then apply the same method.

Step 14 ：\( r^{2} = \frac{160 \pi}{8 \pi} \), \( r = \sqrt{20} \), as a decimal \( r \approx 4.5 \)