The greatest perfect square that is a factor of 396 is 36
Further explanation
Let's recall following formula about Exponents and Surds:
[tex]\boxed { \sqrt { x } = x ^ { \frac{1}{2} } }[/tex]
[tex]\boxed { (a ^ b) ^ c = a ^ { b . c } } [/tex]
[tex]\boxed {a ^ b \div a ^ c = a ^ { b - c } }[/tex]
[tex]\boxed {\log a + \log b = \log (a \times b) }[/tex]
[tex]\boxed {\log a - \log b = \log (a \div b) }[/tex]
Let us tackle the problem.
Firstly , we could factorize 396 as follows :
[tex]396 = 2 \times 198[/tex]
[tex]396 = 2 \times 2 \times 99[/tex]
[tex]396 = 2 \times 2 \times 3 \times 33[/tex]
[tex]396 = 2 \times 2 \times 3 \times 3 \times 11[/tex]
[tex]396 = 2^2 \times 3^2 \times 11[/tex]
Factor of 396 that is perfect square from above results is :
[tex]\boxed{2^2} ~,~ \boxed{3^2} ~or~ \boxed{2^2 \times 3^2}[/tex]
The greatest perfect square is:
[tex]2^2 \times 3^2 = 4 \times 9 = \large {\boxed{36}[/tex]
Learn more
- Coefficient of A Square Root : https://brainly.com/question/11337634
- The Order of Operations : https://brainly.com/question/10821615
- Write 100,000 Using Exponents : https://brainly.com/question/2032116
Answer details
Grade: High School
Subject: Mathematics
Chapter: Exponents and Surds
Keywords: Power , Multiplication , Division , Exponent , Surd , Negative , Postive , Value , Equivalent , Perfect , Square , Factor.
