Largest Number Among the Given Options

The given options are: ³√2, √3, ³√5, and 1.5. We need to determine the largest number among these options.

Comparing the Numbers

To find the largest number among the given options, we can compare them.

- ³√2: The cube root of 2 is approximately 1.26.
- √3: The square root of 3 is approximately 1.73.
- ³√5: The cube root of 5 is approximately 1.71.
- 1.5: This is a decimal number.

Comparing Decimal Numbers

To compare decimal numbers, we can use the following rules:

1. Compare the whole numbers part. If one number has a greater whole number part, it is greater.
2. If the whole numbers part is equal, compare the decimal part. The number with the greater decimal part is greater.

Comparing √3 and ³√5

- √3 has a whole number part of 1 and a decimal part of 0.73.
- ³√5 has a whole number part of 1 and a decimal part of 0.71.

Comparing the decimal parts, we can see that 0.73 is greater than 0.71. Therefore, √3 is greater than ³√5.

Comparing 1.5 with √3

- 1.5 has a whole number part of 1 and a decimal part of 0.5.
- √3 has a whole number part of 1 and a decimal part of 0.73.

Comparing the decimal parts, we can see that 0.73 is greater than 0.5. Therefore, √3 is greater than 1.5.

Final Comparison

From the above comparisons, we can conclude that √3 is the largest number among the given options.

Answer: B) √3