The square root of 6 is expressed together √6 in the radical type and together (6)½ or (6)0.5 in the exponent form. The square source of 6 rounded as much as 7 decimal places is 2.4494897. The is the optimistic solution that the equation x2 = 6.

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Square root of 6: 2.449489742783178Square source 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 uncover the Square root of 6?
4.Important Notes
5.FAQs top top Square root of 6

What Is the Square source of 6?

The square root of a number n is composed as √n. The square root of 6 deserve to be written in different ways.


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

Is the Square source of 6 reasonable or Irrational?

The square root of 6 is one irrational number v non-terminating digits.

How to uncover the Square root of 6?


There are 2 key methods we usage to discover the square root of 6.

Prime Factorization

Prime Factorization

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

Therefore, the square source of 6 is 2.449

Long Division

Step 1: do a pair of number (by put a bar end them) native one's location as shown in the figure.Step 5: The following divisor will certainly be 44 + 4 and thedividendwill be 2400. Us will proceed doing the same measures till we acquire the number of decimals us require.

So ours long division now looks prefer this:

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Therefore, the square root of 6 is 2.449

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Important Notes

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

Solved Examples


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

Solution:

Total surface ar Area is 36cm2Surface Area of every side = 36/6 = 6cm2Edge size = Square root(6) = 2.45 cmTherefore, the edge size of the cube is 2.45cm.


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

Solution:

Distance spanned = speed × TimeTherefore, the human covers a full distance that 6√6 × 1 = 14.697 × 1 = 14.697 miles


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FAQs top top the Square source of 6

What is the worth 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 element factorizing 6 i.e. 21 × 31, 2 is in weird power. Therefore, the square source of 6 is irrational.

What is the Square root of -6?

The square root of -6 is an imagine number. It can be composed as √-6 = √-1 × √6 = i √6 = 2.449iwhere i = √-1 and it is called the imagine unit.

Is the number 6 a Perfect Square?

The element factorization of 6 = 21 × 31. Here, the prime element 2 is no in the pair. Therefore, 6 is not a perfect square.

What is the value of 1 square source 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 source of 6?

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


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