Example Question - cube root calculation
Here are examples of questions we've helped users solve.
Calculating Cube Root and Nearest Integer Estimation
To solve the cube root of 112 and find the integer closest to this value, we will first identify the perfect cubes near 112 to estimate the cube root. The perfect cubes closest to 112 are: - \( 4^3 = 64 \) - \( 5^3 = 125 \) Since 112 is between 64 and 125, we know the cube root of 112 will be between 4 and 5. Because 112 is closer to 125 than it is to 64, the cube root of 112 will be closer to 5. Therefore, the integer closest to \( \sqrt[3]{112} \) is 5.
Cube Root Inequality
To solve the given question, we need to find two numbers that the cube root of 63 falls between. The cube root of a number, \(\sqrt[3]{x}\), is the number which, when multiplied by itself three times, gives the number \(x\). First, we need to look for perfect cubes that are close to 63. We know that \(3^3 = 27\) and \(4^3 = 64\), therefore the cube root of 63 will be slightly less than 4, because 63 is just one less than 64. Thus, \(\sqrt[3]{63}\) is greater than 3 but less than 4. The expression can be written as: \[3 < \sqrt[3]{63} < 4\] Consequently, the boxes should contain the numbers 3 and 4, respectively.
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