Example Question - estimating cube roots
Here are examples of questions we've helped users solve.
Approach to Finding Closest Integer to Cube Root
To solve the question in the image, we need to find the cube root of 572 and then identify the closest integer to this value. Calculating the exact cube root of 572 might be challenging without a calculator, but we can estimate the closest integer by finding the cube roots of perfect cubes near 572. The cube of 8 is \(8^3 = 512\), and the cube of 9 is \(9^3 = 729\). Since 572 falls between 512 and 729, the cube root of 572 will be between 8 and 9. Since 572 is closer to 512 than it is to 729, we can safely say that the cube root of 572 will be closer to 8 than to 9. Therefore, the integer closest to the cube root of 572 is 8.
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.
Determining the Closest Integer to the Cube Root of 55
The question is asking for the closest integer to the cube root of 55. To estimate the cube root of 55, we should find two perfect cubes that 55 falls between. The cube of 3 is \(3^3 = 27\), and the cube of 4 is \(4^3 = 64\). Since 55 is between 27 and 64, the cube root of 55 must be between 3 and 4. Given that the cube root of 55 is \( \sqrt[3]{55} \), and we know that: \(3 < \sqrt[3]{55} < 4\) Since 55 is closer to 64 than it is to 27, the cube root of 55 will be closer to 4 than it is to 3. Therefore, the closest integer to the cube root of 55 is 4.
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