Final answer:
The square root of 24 using perfect squares is found by factoring 24 into 4 and 6, where 4 is a perfect square. The final result is 2 times the square root of 6, which is written as 2√6.
Step-by-step explanation:
To find the square root of 24 using perfect squares, we start by factoring 24 into the product of perfect squares and other integers. We can write 24 as 4 × 6, where 4 is a perfect square (2²). Now we can take the square root of each part separately:
√24 = √(4 × 6) = √4 × √6
Since the square root of 4 is 2, we then have:
2 × √6
The square root of 6 is not a whole number, but we can leave it in the square root form or approximate it to a decimal if required. Therefore, the square root of 24 using perfect squares is 2√6.