The square root of 6 is expressed as √6 in the radical develop and also as (6)½ or (6)0.5 in the exponent develop. The square root of 6 rounded as much as 7 decimal areas is 2.4494897. It is the positive solution of the equation x2 = 6.

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Square Root of 6: 2.449489742783178Square Root of 6 in exponential form: (6)½ or (6)0.5Square Root of 6 in radical form: √6
1.What Is the Square Root of 6?
2.Is the Square Root of 6 Rational or Irrational?
3.How to Find the Square Root of 6?
4.Important Notes
5.FAQs on Square Root of 6

What Is the Square Root of 6?

The square root of a number n is created as √n. The square root of 6 can be written in different methods.


Radical form: √6Decimal form: 2.449Exponent form: (6)1/2

Is the Square Root of 6 Rational or Irrational?

The square root of 6 is an irrational number via non-terminating digits.

How to discover the Square Root of 6?


There are 2 primary techniques we use to uncover the square root of 6.

Prime Factorization

Prime Factorization

Now, let's discover the square root.√6 = √(2 × 3)√6 = √2 × √3= 1.414 × 1.732= 2.449

Because of this, the square root of 6 is 2.449

Long Division

Step 1: Make a pair of digits (by placing a bar over them) from one's area as displayed in the number.Tip 5: The following divisor will be 44 + 4 and thedividendwill certainly be 2400. We will continue doing the exact same measures till we obtain the number of decimals we require.

So our lengthy department currently looks prefer this:

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Because of this, the square root of 6 is 2.449

Explore square roots utilizing illustrations and also interenergetic examples


Important Notes

The square root of 6 = 2.449√6 is irrational and is non-terminating.The square root of 6 has actually 2 actual roots, +2.449 and -2.449

Solved Examples


Example 1: Kate has a cube. The location of all 6 sides of the cube is 36cm2. Aid her calculate the edge length of the cube.

Solution:

Total Surconfront Area is 36cm2Surchallenge Area of each side = 36/6 = 6cm2Edge Length = Square root(6) = 2.45 cmTherefore, the edge length of the cube is 2.45cm.


Example 2: What will certainly be the distance covered by a perboy running at 6√6 miles per hour in 1 hour?

Solution:

Distance covered = Speed × TimeBecause of this, the perboy covers a total distance of 6√6 × 1 = 14.697 × 1 = 14.697 miles


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FAQs on the Square Root of 6

What is the Value of the Square Root of 6?

The square root of 6 is 2.44948.

Why is the Square Root of 6 an Irrational Number?

Upon prime factorizing 6 i.e. 21 × 31, 2 is in odd power. Because of this, the square root of 6 is irrational.

What is the Square Root of -6?

The square root of -6 is an imaginary number. It have the right to be created as √-6 = √-1 × √6 = i √6 = 2.449iwbelow i = √-1 and it is referred to as the imaginary unit.

Is the number 6 a Perfect Square?

The prime factorization of 6 = 21 × 31. Here, the prime factor 2 is not in the pair. Therefore, 6 is not a perfect square.

What is the Value of 1 square root 6?

The square root of 6 is 2.449. Therefore, 1 √6 = 1 × 2.449 = 2.449.

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What is the Square of the Square Root of 6?

The square of the square root of 6 is the number 6 itself i.e. (√6)2 = (6)2/2 = 6.


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