Question - Finding Numbers for Inequality with Cube Root
Solution:
The image shows an inequality with a cube root: \[ \_ < \sqrt[3]{63} < \_ \]We need to fill in the blanks with numbers to make the inequality true. To do so, we need to find two numbers that the cube root of 63 falls between.The cube root of 63 is a bit more than the cube root of 64, which is 4, because 4^3 = 64. Since 63 is less than 64, its cube root will be slightly less than 4.Now let's find two consecutive whole numbers that the cube root of 63 will lie between. We already know that it will be less than 4 and more than 3 because 3^3 = 27 which is much less than 63.So the correct inequality is:\[ 3 < \sqrt[3]{63} < 4 \]This reads as "the cube root of 63 is more than 3 but less than 4."
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