Example Question - cube root inequality
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Completing Cube Root Inequality Statement
The image shows an incomplete mathematical inequality statement that involves a cube root: Complete the following statement. Use < or >. < cube_root(15) < To complete the statement, we need to find two numbers that the cube root of 15 lies between. The cube root of a number is a value that, when multiplied by itself three times, gives the original number. Since we know that the cube root of 8 (2^3) is 2 and the cube root of 27 (3^3) is 3, we can say that the cube root of 15 must lie between 2 and 3, because 15 is between 8 and 27. Therefore, the completed statement is: 2 < cube_root(15) < 3 This reads as "2 is less than the cube root of 15, which is less than 3."
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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