To find the expression equivalent to [tex]\(\sqrt{150}\)[/tex], we need to simplify it by breaking it down into its prime factors and using the properties of square roots.
1. Begin with the given expression:
[tex]\[\sqrt{150}\][/tex]
2. Factorize the number 150:
[tex]\[150 = 25 \times 6\][/tex]
3. Use the property of square roots that allows us to separate the factors:
[tex]\[\sqrt{150} = \sqrt{25 \times 6} = \sqrt{25} \times \sqrt{6}\][/tex]
4. Simplify the square root of 25:
[tex]\[\sqrt{25} = 5\][/tex]
5. Multiply the simplified terms together:
[tex]\[\sqrt{150} = 5 \times \sqrt{6}\][/tex]
Therefore, the expression [tex]\(\sqrt{150}\)[/tex] simplifies to [tex]\(5 \sqrt{6}\)[/tex].
The correct answer is:
[tex]\[5 \sqrt{6}\][/tex]
So, the correct choice is:
[tex]\[4\][/tex]
