use the square root property to determine all real solutions for each of the following equations.

\3p^2 - 216 = 0\

$p =$

\2b^2 + 90 = 0\

$b =$

give exact solutions (dont use decimals), and separate multiple solutions with commas. if there are no real solutions, type dne.

Question

use the square root property to determine all real solutions for each of the following equations.

\3p^2 - 216 = 0\

$p =$

\2b^2 + 90 = 0\

$b =$

give exact solutions (dont use decimals), and separate multiple solutions with commas. if there are no real solutions, type dne.

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Simplifying Radicals" ], "new_concepts": [ "Square Root Property", "Solving Quadratic Equations" ], "current_concepts": [ "Square Root Property", "Simplifying Radicals", "Solving Quadratic Equations" ] } ## Isolate the variable in the first equation $$ \begin{aligned} 3p^2 - 216 &= 0 \ 3p^2 &= 216 \ p^2 &= 72 \end{aligned} $$ ## Apply the square root property to solve for p $$ \begin{aligned} p &= \pm\sqrt{72} \ p &= \pm\sqrt{36 \times 2} \ p &= \pm6\sqrt{2} \end{aligned} $$ ## Solve the second equation for b $$ \begin{aligned} 2b^2 + 90 &= 0 \ 2b^2 &= -90 \ b^2 &= -45 \ b &= \pm\sqrt{-45} otin \mathbb{R} \end{aligned} $$ ## Question 1 $p =$ $6\sqrt{2}, -6\sqrt{2}$ ## Question 2 $b =$ DNE { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Square Root Property" ] }

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QUESTION IMAGE

Question

Explanation:

Isolate the variable in the first equation

Apply the square root property to solve for p

Solve the second equation for b

Answer:

Question 1

Question 2