You are given a cube. If the volume of the cube is 125 in3 , you can find the length of one of the sides by
taking the cube root of the volume.
In this case, the volume is 125 in3.
So, the length of one side of the cube is:
\( \text{side length} = \sqrt[3]{\text{volume}} = \sqrt[3]{125} = 5 \, \text{inches} \)
Therefore, the length of one side of the cube is 5 inches.
Which two perfect squares does √300 lie between?
To find the two perfect squares between which √300 lies, we can calculate the square root of the numbers close to 300.
√289 = 17
√324 = 18
So, √300 lies between 17 and 18 because 17^2 = 289 < 300 < 324 = 18^2.
Therefore, √300 lies between the perfect squares of 17 and 18.
x^2 = 9/121 which statement is true when you solve for x?
To solve for x when given that \(x^2 = \frac{9}{121}\), we can take the square root of both sides of the equation:
\[ x = \pm \sqrt{\frac{9}{121}} \]
To simplify the square root of \(\frac{9}{121}\), we can take the square root of the numerator and the denominator separately:
\[ x = \pm \frac{\sqrt{9}}{\sqrt{121}} = \pm \frac{3}{11} \]
So, the solutions for x are \(x = \frac{3}{11}\) and \(x = -\frac{3}{11}\).
The true statement when you solve for x is:
\[ x = \pm \frac{3}{11} \]