Checking square roots, we see that 13^{2} = 169 and 14^{2} = 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

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.

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