Question - Cube Root Inequality
Solution:
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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