Final answer:
To solve the square root of 300, factor it into its prime factors, simplify under the square root, and then express the exact value as 10√3. This is the most simplified form without converting to a decimal approximation.
Step-by-step explanation:
The square root of 300 can be found by identifying the prime factors and then simplifying. We break down 300 into its prime factors: 300 = 22 × 3 × 52. Using the property of square roots that √(ab) = √(a)√(b), we can say that √300 = √(22√3√52).
This can be simplified to √(22)√(52)√3, which yields 2×5√3 or 10√3. While 10√3 is not a whole number, it is the exact value expression for the square root of 300. For calculations with exponentials, remember that the exponential term can be halved when taking a square root. To practice with square roots and other operations, it is beneficial to get familiar with your calculator functions, as suggested.
To solve the square root of 300 exactly, we can use a calculator or work it out manually. If we use a calculator, we can simply input the number 300 and find the square root function to get the answer. The exact value is approximately 17.3205.