Sure, let's simplify [tex]\(\sqrt{50}\)[/tex] step-by-step.
1. Prime Factorization: First, break down the number 50 into its prime factors.
[tex]\[ 50 = 2 \times 25 = 2 \times 5^2 \][/tex]
2. Rewrite the Square Root: Use the prime factors to rewrite the square root expression.
[tex]\[ \sqrt{50} = \sqrt{2 \times 5^2} \][/tex]
3. Use the Property of Square Roots: Apply the property [tex]\(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\)[/tex].
[tex]\[ \sqrt{2 \times 5^2} = \sqrt{2} \times \sqrt{5^2} \][/tex]
4. Simplify: Since [tex]\(\sqrt{5^2} = 5\)[/tex], you can simplify the expression further.
[tex]\[ \sqrt{2} \times 5 \][/tex]
5. Reorder the Terms: To match conventional mathematical notation, write the number first.
[tex]\[ 5 \sqrt{2} \][/tex]
So, the simplified form of [tex]\(\sqrt{50}\)[/tex] is:
[tex]\[ \sqrt{50} = 5 \sqrt{2} \][/tex]
And if you compute the numerical value of [tex]\(\sqrt{50}\)[/tex], you get approximately:
[tex]\[ \sqrt{50} \approx 7.0710678118654755 \][/tex]
Hence, the simplified result is [tex]\(5 \sqrt{2}\)[/tex] and its numerical value is approximately [tex]\(7.0710678118654755\)[/tex].
