The square root of 18 is denoted by √18 and its simplified radical form is equal to 3√2. The value of root 18 is 4.243 corrected up to 3 decimal places. If x is a square root of 18, then it satisfies the quadratic equation x2 = 18. Let us learn about this here.
Some Facts about Square Root of 18:
- Root 18 in simplest radical form is equal to 3√2.
- √18 = 4.24 in decimal form corrected up to 2 decimal places.
- 18 is not a perfect square.
- 181/2 is the exponential form and √18 is the radical form of the square root of 18.
- Square of 18: 18×18 = 324.
Table of Contents
What is the Square Root of 18?
Solution: To find the square root of 18, we will follow the below steps.
The first step is the following:
| First, we write the number 18 as a product of perfect squares (may not be all). See that we can write 18 = 9 × 2 where 9 is a perfect square as 9 =32. |
The second step is as follows:
| Therefore, $\sqrt{18} = \sqrt{9 \times 2}$ ⇒ √18 = √9 × √2 using the rule: √ab = √a × √b. ⇒ √18 = 3 × √2, since the square root of 9 is 3. ⇒ √18 = 3√2. |
Therefore, the square root of 18 is equal to 3√2, and it is its simplified radical form. That is, √18 = 3√2.
Also Read: Square root of 50
Square Root of 18 by Prime Factorization
The prime factorization of 18 is given by
18 = 2 × 3 × 3.
Now, taking square root on both sides we obtain that
$\sqrt{18} = \sqrt{2 \times 3 \times 3}$.
Making group of two identical numbers, it follows that
$\sqrt{18} = \sqrt{2} \times \sqrt{3 \times 3}$
⇒ √18 = √2 × 3, using the rule: √(a×a) = a.
⇒ √18 = 3√2.
So the simplest radical form of square root of 18 is equal to 3√2, and it is obtained by the prime factorization method.
Square root of 27 | Square root of 32
Value of Root 18
Answer: As √18 = 3√2 and the value of root 2 is equal to 1.414, so it follows that the value of root 18 will be calculated as follows:
√18 = 3√2 = 3 × 1.414 = 4.242.
So the value of square root of 18 is equal to 4.242.
Is 18 Perfect Square?
Answer: The number 18 can be a perfect square if its square root is a whole number. As we know √18 = 3√2 and it is not a whole number, we conclude that 18 is not a perfect square number.
Is Square Root of 18 Rational?
Answer: As the value of root 18 is 3√2, and √2 is an irrational number, we conclude that the square root of 18 is not a rational number.
FAQs
Answer: The simplest radical form of square root of 18 is equal to 3√2, that is, √18 = 3√2.
Answer: 3√2 is the lowest radical form of the square root of 18.
Answer: As 18 cannot be written as a square of an integer, the number 18 is not a perfect square.
Answer: We know √18 = 3√2 and √2 is not a rational number. So square root of 18 is an irrational number.
This article is written by Dr. T, an expert in Mathematics (PhD). On Mathstoon.com you will find Maths from very basic level to advanced level. Thanks for visiting.