Answer :
To find the solutions to the equation [tex]\( x^2 = 18 \)[/tex], we need to follow these steps:
1. Isolate the variable x:
The equation given is [tex]\( x^2 = 18 \)[/tex].
2. Take the square root of both sides:
To solve for [tex]\( x \)[/tex], we take the square root of both sides of the equation. Remember that taking the square root will give us both the positive and negative roots.
[tex]\[ x = \pm \sqrt{18} \][/tex]
3. Simplify the square root of 18:
To simplify [tex]\( \sqrt{18} \)[/tex], we can factor 18 into its prime factors.
[tex]\[ 18 = 9 \times 2 \][/tex]
So, we can write:
[tex]\[ \sqrt{18} = \sqrt{9 \times 2} \][/tex]
Using the property of square roots, [tex]\( \sqrt{a \times b} = \sqrt{a} \times \sqrt{b} \)[/tex], we get:
[tex]\[ \sqrt{18} = \sqrt{9} \times \sqrt{2} \][/tex]
Since [tex]\( \sqrt{9} = 3 \)[/tex], we have:
[tex]\[ \sqrt{18} = 3 \times \sqrt{2} \][/tex]
4. Write the final solutions:
Hence, the solutions to [tex]\( x^2 = 18 \)[/tex] are:
[tex]\[ x = \pm 3\sqrt{2} \][/tex]
So, the correct choice is [tex]\( \boxed{B} \)[/tex].
1. Isolate the variable x:
The equation given is [tex]\( x^2 = 18 \)[/tex].
2. Take the square root of both sides:
To solve for [tex]\( x \)[/tex], we take the square root of both sides of the equation. Remember that taking the square root will give us both the positive and negative roots.
[tex]\[ x = \pm \sqrt{18} \][/tex]
3. Simplify the square root of 18:
To simplify [tex]\( \sqrt{18} \)[/tex], we can factor 18 into its prime factors.
[tex]\[ 18 = 9 \times 2 \][/tex]
So, we can write:
[tex]\[ \sqrt{18} = \sqrt{9 \times 2} \][/tex]
Using the property of square roots, [tex]\( \sqrt{a \times b} = \sqrt{a} \times \sqrt{b} \)[/tex], we get:
[tex]\[ \sqrt{18} = \sqrt{9} \times \sqrt{2} \][/tex]
Since [tex]\( \sqrt{9} = 3 \)[/tex], we have:
[tex]\[ \sqrt{18} = 3 \times \sqrt{2} \][/tex]
4. Write the final solutions:
Hence, the solutions to [tex]\( x^2 = 18 \)[/tex] are:
[tex]\[ x = \pm 3\sqrt{2} \][/tex]
So, the correct choice is [tex]\( \boxed{B} \)[/tex].
