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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 9: Q.8 (page 869)

Solve Quadratic Equations of the Form $a x^{2} = k$
Using the Square Root Property.
In the following exercises, solve each equation $3 n^{2} = 48$

Short Answer

Expert verified

The solution of the quadratic equation: $n = 4, n = - 4$

Step by step solution

01

Step 1. Given information

Consider the quadratic equation $3 n^{2} = 48$

The objective is to solve the quadratic equation by using the square root property. If $x^{2} = k$ , then $x = 卤 \sqrt{k}$

The quadratic term is isolated. Divide by 3 to make its coefficient 1.

$\frac{3 n^{2}}{3} = \frac{48}{3} n^{2} = 16$

02

Step 2. Apply square root property

So, $n = 卤 \sqrt{16}$

Simplify the radical.

$n = 卤 \sqrt{4 路 4} n = 卤 4$

Rewrite to show two solutions.

$n = 4, n = - 4$

03

Step 3. Check the solutions

Substitute $n = 4$ in the original equation

$3 n^{2} = 48 3 {(4)}^{2} \overset{?}{=} 48 3 (16) \overset{?}{=} 48 48 = 48$

Substitute $n = - 4$ in the original equation

$3 n^{2} = 48 3 {(- 4)}^{2} \overset{?}{=} 48 3 (16) \overset{?}{=} 48 48 = 48$

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Most popular questions from this chapter

Solve :- ${(x - 5)}^{2} + 6 (x - 5) + 8 = 0$

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