Square Root of 4100
The square root of 4100 is expressed as √4100 in the radical form and as (4100)½ or (4100)0.5 in the exponent form. The square root of 4100 rounded up to 5 decimal places is 64.03124. It is the positive solution of the equation x2 = 4100. We can express the square root of 4100 in its lowest radical form as 10 √41.
- Square Root of 4100: 64.03124237432849
- Square Root of 4100 in exponential form: (4100)½ or (4100)0.5
- Square Root of 4100 in radical form: √4100 or 10 √41
1. | What is the Square Root of 4100? |
2. | How to find the Square Root of 4100? |
3. | Is the Square Root of 4100 Irrational? |
4. | FAQs |
What is the Square Root of 4100?
The square root of 4100, (or root 4100), is the number which when multiplied by itself gives the product as 4100. Therefore, the square root of 4100 = √4100 = 10 √41 = 64.03124237432849.
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How to Find Square Root of 4100?
Value of √4100 by Long Division Method
Explanation:
- Forming pairs: 41 and 00
- Find a number Y (6) such that whose square is <= 41. Now divide 41 by 6 with quotient as 6.
- Bring down the next pair 00, to the right of the remainder 5. The new dividend is now 500.
- Add the last digit of the quotient (6) to the divisor (6) i.e. 6 + 6 = 12. To the right of 12, find a digit Z (which is 4) such that 12Z × Z <= 500. After finding Z, together 12 and Z (4) form a new divisor 124 for the new dividend 500.
- Divide 500 by 124 with the quotient as 4, giving the remainder = 500 - 124 × 4 = 500 - 496 = 4.
- Now, let's find the decimal places after the quotient 64.
- Bring down 00 to the right of this remainder 4. The new dividend is now 400.
- Add the last digit of quotient to divisor i.e. 4 + 124 = 128. To the right of 128, find a digit Z (which is 0) such that 128Z × Z <= 400. Together they form a new divisor (1280) for the new dividend (400).
- Divide 400 by 1280 with the quotient as 0, giving the remainder = 400 - 1280 × 0 = 400 - 0 = 400.
- Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 4100.
Therefore, the square root of 4100 by long division method is 64.0 approx.
Is Square Root of 4100 Irrational?
The actual value of √4100 is undetermined. The value of √4100 up to 25 decimal places is 64.03124237432848686488218. Hence, the square root of 4100 is an irrational number.
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- Square Root of 1521 - √1521 = 39
- Square Root of 25 - √25 = 5
- Square Root of 240 - √240 = 15.49193
- Square Root of 676 - √676 = 26
Square Root of 4100 Solved Examples
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Example 1: Solve the equation x2 − 4100 = 0
Solution:
x2 - 4100 = 0 i.e. x2 = 4100
x = ±√4100
Since the value of the square root of 4100 is 64.031,
⇒ x = +√4100 or -√4100 = 64.031 or -64.031. -
Example 2: If the area of an equilateral triangle is 4100√3 in2. Find the length of one of the sides of the triangle.
Solution:
Let 'a' be the length of one of the sides of the equilateral triangle.
⇒ Area of the equilateral triangle = (√3/4)a2 = 4100√3 in2
⇒ a = ±√16400 in
Since length can't be negative,
⇒ a = √16400 = 2 √4100
We know that the square root of 4100 is 64.031.
⇒ a = 128.062 in -
Example 3: If the surface area of a cube is 24600 in2. Find the length of the side of the cube.
Solution:
Let 'a' be the length of the side of the cube.
⇒ Area of the cube = 6a2 = 24600 in2
⇒ a = ±√4100 in
Since length can't be negative,
⇒ a = √4100
We know that the square root of 4100 is 64.031.
⇒ a = 64.031 in
FAQs on the Square Root of 4100
What is the Value of the Square Root of 4100?
The square root of 4100 is 64.03124.
Why is the Square Root of 4100 an Irrational Number?
Upon prime factorizing 4100 i.e. 22 × 52 × 411, 41 is in odd power. Therefore, the square root of 4100 is irrational.
What is the Value of 18 square root 4100?
The square root of 4100 is 64.031. Therefore, 18 √4100 = 18 × 64.031 = 1152.562.
Is the number 4100 a Perfect Square?
The prime factorization of 4100 = 22 × 52 × 411. Here, the prime factor 41 is not in the pair. Therefore, 4100 is not a perfect square.
What is the Square Root of -4100?
The square root of -4100 is an imaginary number. It can be written as √-4100 = √-1 × √4100 = i √4100 = 64.031i
where i = √-1 and it is called the imaginary unit.
If the Square Root of 4100 is 64.031. Find the Value of the Square Root of 41.
Let us represent √41 in p/q form i.e. √(4100/100) = 41/10 = 6.403. Hence, the value of √41.0 = 6.403
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