Suare of 3 exponential
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Answer:
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.
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Square Root of 3
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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.
Square Root of 3: 1.7320508075688772
Square Root of 3 in exponential form: (3)½ or (3)0.5
Square Root of 3 in radical form: √3
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: √3
Exponent form: 31/2
Is the Square Root of 3 Rational or Irrational?
The decimal part of the square root 3 is non-terminating. This is the definition of an irrational number.
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 2 to make the dividend 200.
Step 5: The divisor which is 1 here is 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 value
Step 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 is 34 in this case.
Proceeding in the same manner and repeating from step 4, we can calculate the rest of the decimals.
Explore Square Roots using illustrations and interactive examples
Square Root of 4
Square Root of 2
Square Root of 5
Square Root of 9
Square Root of 15
Important Notes
The real roots of √3 are ± 1.732.
The Square root of a perfect square is always a rational whole number and that of other numbers is always irrational. For example, √16 = 4, whereas √17 = 4.1231…
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.
Read More
Solved Examples
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 * Time
Speed = 50√3 = 86.603 km/hr
Time = 1 hr
Using 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 in
Since radius can't be negative,
⇒ r = √3
Step-by-step explanation:
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Answer:
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