Solve the following equation
2y^2-3=53
Solve for y:
2y2-3 = 53
Add + 3 to both sides of the equation
2y2-3 + 3 = 53 + 3
2y2 = 56
Divide each side of the equation by 2
| 2y2 | |
| 2 |
| = |
| 56 |
| 2 |
| y2 = | 56 |
| 2 |
| y = | √56 |
| √2 |
Using our radical expression calculator, we can simplify this
y2 = 28
Take the square root of each side:
√y2= √28
y= = ±√28
Simplify √28
Checking square roots, we see that 52 = 25 and 62 = 36
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 28 checking for integer square root values below:
√28 = √1√28
√28 = √2√14
√28 = √4√7
Find the highest integer square root
The highest factor that has an integer square root is 4
Therefore, we use the product combo √28 = √4√7
Evaluating square roots, we see that √4 = 2
Final Answer
y = ±2√7
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?
y = ±2√7
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
