Understand the equation: Understand the equation. The equation x^2 = 27 means that x is a number which, when squared (multiplied by itself), equals 27.Take square root: Take the square root of both sides of the equation to solve for x. √(x^2) = √27Simplify left side: Simplify the left side of the equation. Since the square root and the square cancel each other out, we get x on the left side. x = √27Simplify right side: Simplify the right side of the equation. 27 is not a perfect square, but it can be expressed as the product of 9 and 3, where 9 is a perfect square. x = √(9 * 3)Take square root of 9: Take the square root of 9, which is a perfect square. x = √9 * √3 x = 3 * √3Recognize final value: Recognize that √3 cannot be simplified further as it is not a perfect square. Therefore, the final value of x is: x = 3√3

Grade 8

Solve equations using cube roots

Full solution

x^2

Understand the equation: Understand the equation. $\newline$ The equation $x^2 = 27$ means that $x$ is a number which, when squared (multiplied by itself), equals $27$ .
Take square root: Take the square root of both sides of the equation to solve for $x$ . $\sqrt{x^2} = \sqrt{27}$
Simplify left side: Simplify the left side of the equation. $\newline$ Since the square root and the square cancel each other out, we get $x$ on the left side. $\newline$ $x = \sqrt{27}$
Simplify right side: Simplify the right side of the equation. $27$ is not a perfect square, but it can be expressed as the product of $9$ and $3$ , where $9$ is a perfect square. $x = \sqrt{9 \times 3}$
Take square root of $\newline$ $9$ : Take the square root of $9$ , which is a perfect square. $\newline$ $x = \sqrt{9} \times \sqrt{3}$ $\newline$ $x = 3 \times \sqrt{3}$
Recognize final value: Recognize that $\sqrt{3}$ cannot be simplified further as it is not a perfect square. $\newline$ Therefore, the final value of $x$ is: $\newline$ $x = 3\sqrt{3}$