What is the Square Root of 18?
Rounding to eight decimal places, the square root of 18 is 4.24264069.
The square root of 18 results in a number that when multiplied by itself gives the value 18. Also, the square root of 18 can be written in different ways:
Square root of 18 in radical form: \(\sqrt{18}\) or \(3\sqrt{2}\)
Square Root of 18 in decimal form: 4.242640687….
Square root of 18 in exponent form: \((18)^{\frac{1}{2}}\) or \((18)^{0.5}\)
How do we Find the Square Root of 18?
We can find the square root of a number by using the prime factorization method. Let us apply this method to find \(\sqrt{18}\) .
Step 1: Find the prime factors of 18
Prime factorization of 18 = 2 × 3 × 3.
Step 2: Make pairs of identical factors.
Write 2 as \(\sqrt{2}\) x \(\sqrt{2}\)
18 = (\(\sqrt{2}\) × \(\sqrt{2}\) ) × 3 × 3
Step 3: Take a factor from each pair and multiply them to get the square root.
\(\sqrt{18}\) = \(\sqrt{2}\) × 3
\(\Rightarrow~\sqrt{18}\) = \(3\sqrt{2}\)
Since the value of \(\sqrt{2}\) = 1.414 (approx.)
\(\sqrt{18}\) = 3 × 1.414 = 4.242 (approx.)
So, the square root of 18 is \(3\sqrt{2}\) or about 4.242.
Note: The simplest radical form of square root of 18 is \(3\sqrt{2}\).
Definition of Negative Square Root
Each positive number has two square roots, one is positive and the other is negative, as both the positive and negative numbers have the same absolute value.
Let us understand this with an example,
\(3\sqrt{2}\times 3\sqrt{2}\) = 18
\((-3\sqrt{2})\times (-3\sqrt{2})\) = 18
[Since, multiplying two negatives results in a positive)]
From the above the square of \(-3\sqrt{2}\) is 18 and the square of \(3\sqrt{2}\) is also 18. So, we can say that square roots of 18 are both \(3\sqrt{2}\) and \(-3\sqrt{2}\).
Hence, \(\sqrt{18}\) = ± \(3\sqrt{2}\).
Solved Square Root of 18 Examples
Example 1: Find the value of \((3\sqrt{18}\times \sqrt{2})+(\sqrt{18}\times \sqrt{2})\).
Solution:
Expression: \((3\sqrt{18}\times \sqrt{2})+(\sqrt{18}\times \sqrt{2})\) .
\((3\sqrt{18}\times \sqrt{2})+(\sqrt{18}\times \sqrt{2})\) = \((3 \times 3\sqrt{2}\times \sqrt{2})+(3\sqrt{2}\times \sqrt{2})\) [Substitute \(\sqrt{18}=3\sqrt{2}\)]
= (9 × 2) + (3 × 2) [Simplify]
= 18 + 6 [Multiply]
= 24 [Add]
Therefore, the value of the given expression is 24.
Example 2: Evaluate 5 times \(\sqrt{18}\).
Solution:
5 times \(\sqrt{18}\) can be written as:
5 × \(\sqrt{18}\)
Substitute 4.242 for \(\sqrt{18}\)
5 × \(\sqrt{18}\) = 5 × 4.242
= 21.21 [Multiply]
Hence, the value of 5 multiplied by \(\sqrt{18}\) is about 21.21.
Example 3: Samuel wishes to paint the square shaped wall of his room. The wall is spread over 18 square feet. What is the measure of the side length of the wall?
Solution:
The area of the wall is 18 square feet.
We know that,
The area of a square = side \(\times\) side
So, 18 = \(side^2\)
To find the side of the square wall, we will have to find the square root of 18, that is,
\(\sqrt{18}\) = ± \(3\sqrt{2}\).
The length cannot be negative.
Hence, the side length of the wall is \(3\sqrt{2}\) feet.
A number is said to be a perfect square if the square root of the number is an integer.
Yes , the product of two perfect squares is always a perfect square.
Example: Let us take two perfect square numbers, 25 and 36. Their product, 36 x 25 = 900, which is a perfect square as the square root of 900 is 30.
The square root of 18 is 4.2426… which is not an integer so 18 is not a perfect square.
The square root of 18 is 4.2426… which is a non-terminating and non-repeating value so it is an irrational number.