The square root of 3 is expressed as √3 in the radical form and as (3)½ or (3)0.5 in the exponent form. The square root of 3 rounded up to 7 decimal places is 1.7320508. It is the positive solution of the equation x2 = 3.

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What is the Square Root of 3?

The square root of a number is a number which when multiplied by itself, results in the original number. For example, the square root of 25 is 5, as 5 times 5 results in 25. However, you can also have square roots of some numbers that do not result in whole numbers, such as 3. We can express the square root of 3 in different ways


Decimal form: 1.732.Radical form: √3Exponent form: 31/2

Is the Square Root of 3 Rational or Irrational?

Looking at the decimal form of the root 3, we see that it is never-ending -√3 = 1.732050807…….Therefore, we can conclude that Square Root of 3 is Irrational

How to Find the Square Root of 3?

Since we concluded that the square root of 3 is non-terminating, we can only use the long-division method to calculate its value.


Step 1: To begin, we write 3 as 3.000000 and group the 0s after the decimal point in pairs of 2 from left to right as shown below. (for digits to the left of the decimal point, pair them from right to left)Step 2: Think of a number which when multiplied with itself, is less than or equal to 3. In this case, that number would be 1.Step 3: Dividing by 3 by 1 with quotient set as 1, we get a remainder of 2.Step 4:Drag a pair of 0’s down and fill it next to 2to make the dividend 200.Step 5: The divisor which is 1 hereis added with itself and written below. Now, we have 2X as the new divisor, and we need to find a value of X that makes the product of 2X × X less than or equal to 200. In this case, 27 is the required valueStep 6: The number 7 is placed in the quotient after a decimal place. The new divisor for the next division will be 2X + X, which is34 in this case.Proceeding in the same manner and repeating from step 4, we can calculate the rest of the decimals.

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Important Notes

The real roots of √3 are ± 1.732.

Challenging Questions

Find the value of √√3.What is the side length of a square with an area of 10? (Hint: Use long division method)Determine the square root of 33.

Solved Examples


Example 1

John was wondering whether the value of -√3 is the same as √-3. What do you think?


Solution

Negative square roots cannot be real numbers.-√3 is a real number.But √-3 is an imaginary number.Hence, they are not the same, and -√3 is not the same as √-3.


Example 2

Micheal is travelling down the highway at an average speed of 50√3 km/hr for exactly 1 hour. How much distance does he cover?

Solution

We need to use the formula Distance = Speed * TimeSpeed = 50√3 = 86.603 km/hrTime = 1 hrUsing the formula, Distance = 86.603 * 1 = 86.603

Therefore, Micheal covers a distance of 86.603 km


Example: If the area of a circle is 3π in2. Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.⇒ Area of the circle = πr2 = 3π in2⇒ r = ±√3 inSince radius can't be negative,⇒ r = √3The square root of 3 is 1.732.⇒ r = 1.732 in


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FAQs on the Square Root of 3

What is the Value of the Square Root of 3?

The square root of 3 is 1.73205.

Why is the Square Root of 3 an Irrational Number?

The number 3 is prime. This implies that the number 3 is pairless and is not in the power of 2. Therefore, the square root of 3 is irrational.

If the Square Root of 3 is 1.732. Find the Value of the Square Root of 0.03.

Let us represent √0.03 in p/q form i.e. √(3/100) = 0.03/10 = 0.173. Hence, the value of √0.03 = 0.173

Evaluate 14 plus 16 square root 3

The given expression is 14 + 16 √3. We know that the square root of 3 is 1.732. Therefore, 14 + 16 √3 = 14 + 16 × 1.732 = 14 + 27.713 = 41.713

Is the number 3 a Perfect Square?

The number 3 is prime. This implies that the square root of 3 cannot be expressed as a product of two equal integers. Therefore, the number 3 is not a perfect square.

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What is the Square Root of 3 in Simplest Radical Form?

The number 3 is a prime number. This implies that the number 3 is pairless and is not in the power of 2. Therefore, the radical form of square root of 3 cannot be simplified further.