Sure, let's delve into the given mathematical expression step by step. We'll explore if the equation [tex]\(\sqrt{6} = 3\)[/tex] is true.
1. Understanding the Square Root:
The square root of a number [tex]\(x\)[/tex] is a value [tex]\(y\)[/tex] such that [tex]\(y^2 = x\)[/tex]. In this case, we need to check if there is a number [tex]\(y\)[/tex] such that [tex]\(y^2 = 6\)[/tex] and [tex]\(y = 3\)[/tex].
2. Verify the Square Root Calculation:
- First, let's find the value of [tex]\(\sqrt{6}\)[/tex].
- The true value of [tex]\(\sqrt{6}\)[/tex] turns out to be approximately [tex]\(2.449489742783178\)[/tex].
3. Compare with 3:
- Now, we compare the calculated square root value [tex]\(\sqrt{6}\)[/tex] with 3.
- Clearly, [tex]\(2.449489742783178\)[/tex] is not equal to 3.
4. Conclusion:
- Thus, the initial equation [tex]\(\sqrt{6} = 3\)[/tex] is incorrect.
- The actual value of [tex]\(\sqrt{6}\)[/tex] is approximately [tex]\(2.449489742783178\)[/tex], and it is not equal to 3.
Hence, the equation [tex]\(\sqrt{6} = 3\)[/tex] is not true. The square root of 6 is approximately [tex]\(2.449489742783178\)[/tex], which is not equal to 3.
