9B Coreq

In the next preview assignment and in the next class, you will need to calculate quantities involving square roots and fractions using the correct order of operations and solve equations involving square roots and fractions.
Solving Equations Containing Square Roots and Fractions

When solving equations containing square roots or fractions, use the following  properties:

  • [latex](\sqrt{a})^{2} = a[/latex] for any real number where [latex]a \geq 0[/latex]
  • [latex]b \times \frac{c}{b} = c[/latex] for any real number where [latex]b \neq 0[/latex]

Question 1

Consider the equation [latex]\sqrt{x}=5[/latex]. Assume that [latex]x \geq 0[/latex]. Solve this equation by squaring both sides and then using the property [latex](\sqrt{a})^{2}=a[/latex] to simplify the left side.

Question 2

Consider the equation [latex]\sqrt{8y}=4[/latex]. Assume that [latex]y \geq 0[/latex].

  1. Rewrite this equation by squaring both sides and then using the property [latex](\sqrt{a})^{2} = a[/latex] to simplify the left side.
  2. Use your work from Part a to determine the solution for [latex]y[/latex]. In other words, use algebra to get [latex]y[/latex] by itself on one side of the equation.

Question 3

Consider the equation [latex]\sqrt{w}=\frac{1}{4}[/latex]. Assume that [latex]w \geq 0[/latex].

  1. Rewrite this equation by multiplying both sides by 4 and then using the property [latex]b \times \frac{c}{b} = c[/latex] to simplify the right side of the equation.
  2. Use your work from Part a to solve this equation for [latex]w[/latex] by squaring both sides and then dividing both sides by 16.

Question 4

Consider the equation [latex]6=\sqrt{\frac{9}{n}}[/latex]. Assume that [latex]n \geq 0[/latex].

  1. Rewrite this equation by squaring both sides and then using the property  [latex](\sqrt{a})^{2} = a[/latex] to simplify the right side of the equation.
  2. Using your work from Part a, multiply both sides by [latex]n[/latex] and use the property [latex]b \times \frac{c}{b} = c[/latex] to simplify the left side. Then solve for [latex]n[/latex], writing your solution as a simplified fraction.

Practice

Solve each of the following equations for the variable. After you find the solution, substitute the solution back into the equation to check your work.

Question 5

[latex]\frac{12}{x}=3[/latex], where [latex]x \neq 0[/latex]

Question 6

[latex]\sqrt{\frac{1}{3}p}=5[/latex], where [latex]p \geq 0[/latex]

Question 7

[latex]\sqrt{\frac{0.5}{m}}=0.2[/latex]