Question

homework 9: section 2.5
score: 130/280 answered: 13/28
question 16
solve for ( x ) using the square root property.
( n^2 = 45 )
( n = )
entry tip: do not use a decimal approximation for square roots. to enter a number like ( 5sqrt{7} ), type 5*sqrt(7). preview your answer before submitting!
furthere tip: write your answers as a list, with your answers separated by (a) comma(s). for example, if you get 4 and ( -\frac{2}{3} ) as your answers, then enter 4,-2/3 in the box.
question help: message instructor

Explanation:

Step1: Apply square root property

The square root property states that if \( x^2 = a \), then \( x=\pm\sqrt{a} \). For the equation \( n^2 = 45 \), we take the square root of both sides.
\( n=\pm\sqrt{45} \)

Step2: Simplify the square root

Simplify \( \sqrt{45} \). We can factor 45 as \( 9\times5 \), and since \( \sqrt{9\times5}=\sqrt{9}\times\sqrt{5} = 3\sqrt{5} \). So \( \sqrt{45}=3\sqrt{5} \).
Thus, \( n = 3\sqrt{5},- 3\sqrt{5} \)

Answer:

\( 3\sqrt{5},-3\sqrt{5} \)