**Radical Equations**

**Unit 7 Problems**

**Application problems including radical equations.**

1. A positive real number is 4 less than another. When 8 times the larger is added to the square of the smaller, the result is 96. Find the numbers.

__Solution__

Let one number be x

The other number is x+4

8(x+4) + x^{2} = 96

8x+32x^{2} = 96

x^{2} + 8x - 64= 0

x^{2} + 8x +16 = 80

(x+4)^{2} = 80

x = -4-4√5

or x = -4+4√5

2. A positive real number is 4 less than another. If the sum of the squares of the two numbers is 72, then find the numbers.

__Solution__

Let one number be x

The other number is x+4

(x+4)^{2} + x^{2} = 72

x^{2}+x^{2} + 8x + 16 = 72

x^{2} + 4x – 28 = 0

x^{2} + 4x = 28

(x+2)^{2} = 32

x = -2±√32

x= -2+√32

or x = -2+√32

3. The area of a rectangle is 46 square inches. If the length is 4 times the width, then find the dimensions of the rectangle. Round off your answers to the nearest hundredth.

__Solution__

x(4x) = 46

x^{2} - 46 = 0

4x^{2} = 46

x^{2} = 23

x^{2} = 11.5

x = -3.39

or

x = 3.39

ignore -3.39

Hence, the dimensions are;

Length = 3.39x4 =13.56 Inches

Width = 3.39 Inches.

4. If the sides of a square measure units, then find the length of the diagonal.

__Solution__

Let the length of the diagonal be x

X^{2} = (9√3)^{2} + (9√3)^{2}

X^{2} = (81x3) + (81x3)

X^{2} = 486

X = 22.05 Units

5. The area of a rectangle is 20 square inches. If the length is 4 inches less than 6 times the width, then find the dimensions of the rectangle. Round off your answers to the nearest hundredth.

__Solution__

Let the width be x

Length = 6x-4

x(6x-4) = 20

x^{2}-x-=0

(x-)=

Either x = -1.52(ignore)

Or x = 2.19

Length = 6(2.19)-4 = 9.14 Inches.

Width = 2.19 Inches.

To export a reference to this article please select a referencing stye below.

Assignment Hippo (2022) . Retrive from https://assignmenthippo.com/sample-assignment/radical-equations-problem

"." Assignment Hippo ,2022, https://assignmenthippo.com/sample-assignment/radical-equations-problem

Assignment Hippo (2022) . Available from: https://assignmenthippo.com/sample-assignment/radical-equations-problem

[Accessed 14/08/2022].

Assignment Hippo . ''(Assignment Hippo,2022) https://assignmenthippo.com/sample-assignment/radical-equations-problem accessed 14/08/2022.

Want to order fresh copy of the **Sample Template Answers? ** online or do you need the old solutions for Sample Template, contact our customer support or talk to us to get the answers of it.

Our motto is deliver assignment on Time. Our Expert writers deliver quality assignments to the students.

Get reliable and unique assignments by using our 100% plagiarism-free.

Get connected 24*7 with our Live Chat support executives to receive instant solutions for your assignment.

Get Help with all the subjects like: Programming, Accounting, Finance, Engineering, Law and Marketing.

Get premium service at a pocket-friendly rate at AssignmentHippo

- Assignment Writing Guide
- Essay Writing Guide
- Dissertation Writing Guide
- Research Paper Writing Guide

- Accounts
- Computer Science
- Economics
- Engineering

Tap to ChatGet instant assignment help