Final answer:
5√3 is between 5 and 10 because the square root value of 3 is between 2 and 3, and when multiplied by 5, the result falls between 5(2) = 10 and 5(3) = 15. However, 5√3 is actually slightly over 8.5, showing it falls between 5 and 10.
Step-by-step explanation:
The question asks why 5√3 is between 5 and 10. To understand this, we can use the concept of square roots and basic estimation. The square root of a number x can be represented as x raised to the power of 0.5. Therefore, √3 is the same as 30.5. Knowing that the square root of 4 is 2, and the square root of 9 is 3, we can estimate that √3 is somewhere between 2 and 3 since 3 is between 4 and 9.
Now, if we multiply this by 5 (5√3), since √3 is between 2 and 3, multiplying by 5 should give us a number between 10 (5×2) and 15 (5×3). However, the exact value of √3 is slightly over 1.7, meaning that 5√3 is slightly over 8.5. Therefore, 5√3 is not just between 5 and 15 but more precisely between 5 and 10.
Hence, this demonstrates the power of understanding numerical estimation and recognizing the role of the square root as a fractional power. By understanding the simple concept that x2 = √x, we can estimate the values of numbers involving square roots and comprehend their positioning between two integers.