Solve for x: x^2 = 27

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have to solve x^2 = 27 for x.

x^2 = 27

=> x^2 = 9*3

=> x^2 = 3^2 * 3

=> x = 3* sqrt 3 and - 3*sqrt 3

The required value is x = 3* sqrt 3 and x = -3*sqrt 3

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll have to solve the quadratic equation:

x^2 = 27

We'll take square root both sides:

sqrt x^2 = sqrt 27

We'll write 27 = 3^3 = 3*3^2

|x| = 3sqrt3

The solutions of the equation are: {-3sqrt3 ; +3sqrt3}.

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dumore | Student, Undergraduate | (Level 1) eNoter

Posted on

There are two answers…

x² = 27       27 can be expressed as a factor of perfect square 9 and 3
x² = 9*3 , by extracting the square root, we get both + and - solutions
Square root of 9 is +3 , square root of 3 is not perfect whole, so we can leave it as is
x = 3 ±√3
x = 3√3, -3√3

x = 5.196152423, -5.196152423.

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