Example Question - closest integer
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.
Determining Closest Integer to Cube Root
The image is asking for the integer closest to the cube root of 111. To solve this, we should look for two perfect cubes that are close to 111 and then find their cube roots. We know that: - \(4^3 = 64\) - \(5^3 = 125\) Since 111 is between 64 and 125, the cube root of 111 must be between 4 and 5. As 111 is closer to 125 than to 64, the cube root of 111 is closer to 5 than to 4. Hence, the closest integer to \(\sqrt[3]{111}\) is 5.
Finding the Closest Cube Root to 111
The image contains a question asking which integer is closest to the cube root of 111. To answer this, let's look for perfect cubes near 111 and find their cube roots. - The perfect cube closest to 111 that is less than it is \( 4^3 = 64 \). - The next perfect cube greater than 111 is \( 5^3 = 125 \). Since 111 is closer to 125 than to 64, we can say that the cube root of 111 is closer to 5 than to 4. Thus, the integer closest to the cube root of 111 is 5.
Finding Closest Integer to Cube Root
The expression in the question is the cube root of √2, which can be rewritten using exponents as (2^(1/2))^(1/3). When we multiply the exponents, we get 2^(1/6). To find out which integer this is closest to, we can look for small integers and their sixth powers to compare. The sixth power of 1 is 1 (since 1^6 = 1), and the sixth power of 2 is 64 (since 2^6 = 64). The number 2^(1/6) will be somewhere between 1 and 2, but closer to 1 since 2 is much larger when raised to the sixth power. Therefore, the integer closest to the cube root of √2 is 1.
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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