Solve the following equation
2w^2=360
Solve for w:
2w2 = 360
Divide each side of the equation by 2
| 2w2 | |
| 2 |
| = |
| 360 |
| 2 |
| w2 = | 360 |
| 2 |
| w = | √360 |
| √2 |
Using our radical expression calculator, we can simplify this
w2 = 180
Take the square root of each side:
√w2= √180
w= = ±√180
Simplify √180
Checking square roots, we see that 132 = 169 and 142 = 196
Our answer is not an integer, so we try simplify it into the product of an integer and a radical.
We do this by listing each product combo of 180 checking for integer square root values below:
√180 = √1√180
√180 = √2√90
√180 = √3√60
√180 = √4√45
√180 = √5√36
√180 = √6√30
√180 = √9√20
√180 = √10√18
√180 = √12√15
Find the highest integer square root
The highest factor that has an integer square root is 36
Therefore, we use the product combo √180 = √36√5
Evaluating square roots, we see that √36 = 6
Final Answer
w = ±6√5
Common Core State Standards In This Lesson
6.EE.B.5, 6.EE.B.7, 8.EE.A.2, 8.EE.C.7.B, HSA.CED.A.1, HSA.REI.A.1, HSA.REI.A.2, HSA.REI.B.3, HSA.REI.B.4.B
What is the Answer?
w = ±6√5
How does the Equation and Inequalities Calculator work?
Free Equation and Inequalities Calculator - Solves an equation or inequality with 1 unknown variable and no exponents as well as certain absolute value equations and inequalities such as |x|=c and |ax| = c where a and c are constants. Solves square root, cube root, and other root equations in the form ax^2=c, ax^2 + b = c. Also solves radical equations in the form asqrt(bx) = c. Also solves open sentences and it will solve one step problems and two step equations. 2 step equations and one step equations and multi step equations
This calculator has 1 input.
This calculator has 1 input.
What 3 formulas are used for the Equation and Inequalities Calculator?
One Step Equations (Division):
cx = b
x = b/c
One Step Equations (Addition): x + c = b x = b - c
One Step Equations (Subtraction): x - c = b x = b + c
One Step Equations (Addition): x + c = b x = b - c
One Step Equations (Subtraction): x - c = b x = b + c
What 4 concepts are covered in the Equation and Inequalities Calculator?
- equation
- a statement declaring two mathematical expressions are equal
- equation and inequalities
- unknown
- a number or value we do not know
- variable
- Alphabetic character representing a number
