To find the approximate value of [tex]\(\sqrt{104}\)[/tex], let's follow these steps:
1. Understanding Square Roots: The square root of a number [tex]\(x\)[/tex] is a number [tex]\(y\)[/tex] such that [tex]\(y^2 = x\)[/tex].
2. Estimate: First, let's roughly estimate where [tex]\(\sqrt{104}\)[/tex] lies. We know that:
- [tex]\(\sqrt{100} = 10\)[/tex] (since [tex]\(10^2 = 100\)[/tex])
- [tex]\(\sqrt{121} = 11\)[/tex] (since [tex]\(11^2 = 121\)[/tex])
So, [tex]\(\sqrt{104}\)[/tex] should be between 10 and 11.
3. Closer Approximation: To narrow it down further, let's determine which of the given options is the closest:
- Option (1): [tex]\( 10.2 \)[/tex]
- Option (2): [tex]\( 12 \)[/tex]
- Option (3): [tex]\( 13.5 \)[/tex]
- Option (4): [tex]\( 15 \)[/tex]
4. Comparing with Estimates: Based on our initial estimation between 10 and 11, clearly:
- 12 is too high,
- 13.5 is much higher, and
- 15 is even higher.
The option [tex]\(10.2\)[/tex] is within the range and closely matches our estimation between 10 and 11.
Thus, the approximate value of [tex]\(\sqrt{104}\)[/tex] is [tex]\(10.2\)[/tex], and the correct choice is:
(1) 10.2
