To solve the expression [tex]\(5 \sqrt{2}\)[/tex], we need to go through a few steps carefully to ensure we arrive at the correct answer.
1. Understanding the Square Root:
- First, we need the value of [tex]\(\sqrt{2}\)[/tex], which is the principal square root of 2. This is a known irrational number approximately equal to 1.4142135623730951.
2. Multiplication by 5:
- Once we have [tex]\(\sqrt{2}\)[/tex] as approximately 1.4142135623730951, we proceed by multiplying this value by 5:
[tex]\[
5 \times 1.4142135623730951
\][/tex]
3. Performing the Multiplication:
- We multiply the values:
[tex]\[
5 \times 1.4142135623730951 \approx 7.0710678118654755
\][/tex]
Therefore, multiplying 5 by the square root of 2, [tex]\(5 \sqrt{2}\)[/tex], approximately equals 7.0710678118654755.
