Square Root of 18: Simplified Radical Form

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.
• 18^1/2 is the exponential form and √18 is the radical form of the square root of 18.
• Square of 18: 18×18 = 324.

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.

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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.

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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.

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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.

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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.

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