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Chapter 9: Problem 26

Solve equation by using the square root property. Simplify all radicals. \(3 p^{2}=10\)

Short Answer

Expert verified
p = \pm \frac{\sqrt{30}}{3}

Step by step solution

01

- Isolate the squared term

Divide both sides of the equation by 3 to isolate the squared term. This gives us:\[ p^2 = \frac{10}{3} \]
02

- Apply the square root property

Take the square root of both sides of the equation to solve for \(p\). Remember to consider both the positive and negative roots. This gives us:\[ p = \pm \sqrt{\frac{10}{3}} \]
03

- Simplify the radical

Simplify the radical expression \(\sqrt{\frac{10}{3}}\). Write it as:\[ p = \pm \frac{\sqrt{10}}{\sqrt{3}} \]To rationalize the denominator, multiply the numerator and the denominator by \(\sqrt{3}\), which yields:\[ p = \pm \frac{\sqrt{10} \cdot \sqrt{3}}{\sqrt{3} \cdot \sqrt{3}} = \pm \frac{\sqrt{30}}{3} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

square root property
The square root property is an essential tool for solving quadratic equations. It states that if you have an equation of the form

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Most popular questions from this chapter

Solve each quadratic equation for complex solutions by the quadratic formula. Write solutions in standard form. $$ m^{2}-2 m+2=0 $$

Solve each quadratic equation for complex solutions by the square root property, with \(k<0 .\) Write solutions in standard form. $$ (x+6)^{2}=-7 $$

Solve equation by using the square root property. Simplify all radicals. \(2 t^{2}+7=61\)

Solve equation by using the square root property. Simplify all radicals. \((4 x-3)^{2}=9\)

Given \(f(x)=2 x^{2}-5 x+3,\) find each of the following. $$ f(0) $$
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