Question 1:
For this case we have to simplify the following expression:
[tex]\sqrt {54n ^ 7}[/tex]
We can rewrite the 54 as:
[tex]54 = 9 * 6 = 3 ^ 2 * 6[/tex]
In addition, we have to:
[tex]n ^ 7 = n ^ 6 * n[/tex] (According to the multiplication of powers of the same base)
Also, by definition of properties of powers and roots we have to:
\sqrt [n] {a ^ m} = a ^ (\frac {m} {n})
Then, we can rewrite the expression as:
[tex]\sqrt {3 ^ 2 * n ^ 6 * 6 * n} =\\3n ^ 3 \sqrt {6n}[/tex]
Answer:
Option C
Question 2:
For this case we have by definition, that a perfect square is the result of multiplying a number by itself. Also, the perfect squares are the numbers that have exact square roots.
So:
2 and 10 are not perfect squares.
Answer:
Option A and D
Question 3:
For this case we must simplify the following expression:
[tex]\sqrt {75x ^ 2 * y ^ 4}[/tex]
We can rewrite the 75 as:[tex]75 = 25 * 3 = 5 ^ 2 * 3[/tex]
Also we have that by definition of properties of powers and roots that:
[tex]\sqrt [n] {a ^ m} = a ^ (\frac {m} {n})[/tex]
So, we rewrite the expression:
[tex]\sqrt {5 ^ 2 * x ^ 2 * y ^ 4 * 3} =\\5xy ^ 2 \sqrt {3}[/tex]
Answer:
Option B
