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Extracting square root of x²=32

Sagot :

MindOverMatteridn

The solution for x are $x = \pm 4\sqrt{2}$ or $ x = \: 4\sqrt{2} $ and $ x = - \: 4\sqrt{2} $

Solution:

To extract the square root of the equation $ {x}^{2} = 32 $, follow these steps:

Step 1: Understand the Equation

  • The equation $ {x}^{2} = 32 $ means that x is a number whose square is 32.

Step 2: Take the Square Root

  • To solve for x, take the square root of both sides:

[tex] \sqrt{ {x}^{2} } = \sqrt{32} [/tex]

Step 3: Simplify the Square Root

  • x² can be now x
  • The square root of 32 can be simplified by factoring it out because 32 is not a perfect square, hence:

[tex]\sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \times \sqrt{2} = 4\sqrt{2}[/tex]

Thus, the solutions for x are:

[tex]x = \pm \: 4 \sqrt{2} [/tex]

This means that $ x $ can be either $ 4\sqrt{2} $ or $ -4\sqrt{2} $.