Answer
- The square root of 3249 is 57.
- The square root of 225 is 15.
Solution
- We are asked to calculate the square root of the two numbers below:
1. 3249
2. 225
- We can do this by finding the prime factorization of both numbers.
[tex]\begin{gathered} 3249=3\times3\times19\times19=3^2\times19^2 \\ 225=3\times3\times5\times5=3^2\times5^2 \end{gathered}[/tex]- Since we know that:
[tex]\begin{gathered} \sqrt[]{a^2}=a \\ \text{And}\ldots \\ \sqrt[]{ab}=\sqrt[]{a}\times\sqrt[]{b} \end{gathered}[/tex]- We can thus proceed to solve the questions:
Question 1
[tex]\begin{gathered} \sqrt[]{3249}=\sqrt[]{3^2\times19^2} \\ we\text{ can rewrite this as:} \\ \sqrt[]{3249}=\sqrt[]{3^2}\times\sqrt[]{19^2} \\ \\ \sqrt[]{3249}=3\times19 \\ \\ \therefore\sqrt[]{3249}=57 \end{gathered}[/tex]Question 2:
[tex]\begin{gathered} \sqrt[]{225}=\sqrt[]{3^2\times5^2} \\ \sqrt[]{225}=\sqrt[]{3^2}\times\sqrt[]{5^2} \\ \\ \sqrt[]{225}=3\times5=15 \end{gathered}[/tex]Final Answer
- The square root of 3249 is 57.
- The square root of 225 is 15.
