Square Root of 401
The square root of 401 is expressed as √401 in the radical form and as (401)½ or (401)0.5 in the exponent form. The square root of 401 rounded up to 5 decimal places is 20.02498. It is the positive solution of the equation x2 = 401.
- Square Root of 401: 20.024984394500787
- Square Root of 401 in exponential form: (401)½ or (401)0.5
- Square Root of 401 in radical form: √401
1. | What is the Square Root of 401? |
2. | How to find the Square Root of 401? |
3. | Is the Square Root of 401 Irrational? |
4. | FAQs |
What is the Square Root of 401?
The square root of 401, (or root 401), is the number which when multiplied by itself gives the product as 401. Therefore, the square root of 401 = √401 = 20.024984394500787.
☛ Check: Square Root Calculator
How to Find Square Root of 401?
Value of √401 by Long Division Method
Explanation:
- Forming pairs: 04 and 01
- Find a number Y (2) such that whose square is <= 4. Now divide 04 by 2 with quotient as 2.
- Bring down the next pair 01, to the right of the remainder 0. The new dividend is now 1.
- Add the last digit of the quotient (2) to the divisor (2) i.e. 2 + 2 = 4. To the right of 4, find a digit Z (which is 0) such that 4Z × Z <= 1. After finding Z, together 4 and Z (0) form a new divisor 40 for the new dividend 1.
- Divide 1 by 40 with the quotient as 0, giving the remainder = 1 - 40 × 0 = 1 - 0 = 1.
- Now, let's find the decimal places after the quotient 20.
- Bring down 00 to the right of this remainder 1. The new dividend is now 100.
- Add the last digit of quotient to divisor i.e. 0 + 40 = 40. To the right of 40, find a digit Z (which is 0) such that 40Z × Z <= 100. Together they form a new divisor (400) for the new dividend (100).
- Divide 100 by 400 with the quotient as 0, giving the remainder = 100 - 400 × 0 = 100 - 0 = 100.
- Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 401.
Therefore, the square root of 401 by long division method is 20.0 approx.
Is Square Root of 401 Irrational?
The actual value of √401 is undetermined. The value of √401 up to 25 decimal places is 20.02498439450078572769721. Hence, the square root of 401 is an irrational number.
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- Square Root of 54 - √54 = 7.34847
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- Square Root of 288 - √288 = 16.97056
- Square Root of 250 - √250 = 15.81139
- Square Root of 49 - √49 = 7
- Square Root of 22 - √22 = 4.69042
- Square Root of 39 - √39 = 6.24500
Square Root of 401 Solved Examples
-
Example 1: Solve the equation x2 − 401 = 0
Solution:
x2 - 401 = 0 i.e. x2 = 401
x = ±√401
Since the value of the square root of 401 is 20.025,
⇒ x = +√401 or -√401 = 20.025 or -20.025. -
Example 2: If the area of a circle is 401π in2. Find the radius of the circle.
Solution:
Let 'r' be the radius of the circle.
⇒ Area of the circle = πr2 = 401π in2
⇒ r = ±√401 in
Since radius can't be negative,
⇒ r = √401
The square root of 401 is 20.025.
⇒ r = 20.025 in -
Example 3: If the surface area of a sphere is 1604π in2. Find the radius of the sphere.
Solution:
Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr2 = 1604π in2
⇒ r = ±√401 in
Since radius can't be negative,
⇒ r = √401
The square root of 401 is 20.025.
⇒ r = 20.025 in
FAQs on the Square Root of 401
What is the Value of the Square Root of 401?
The square root of 401 is 20.02498.
Why is the Square Root of 401 an Irrational Number?
The number 401 is prime. This implies that the number 401 is pairless and is not in the power of 2. Therefore, the square root of 401 is irrational.
What is the Square Root of 401 in Simplest Radical Form?
The number 401 is a prime number. This implies that the number 401 is pairless and is not in the power of 2. Therefore, the radical form of square root of 401 cannot be simplified further.
What is the Value of 12 square root 401?
The square root of 401 is 20.025. Therefore, 12 √401 = 12 × 20.025 = 240.300.
Evaluate 15 plus 12 square root 401
The given expression is 15 + 12 √401. We know that the square root of 401 is 20.025. Therefore, 15 + 12 √401 = 15 + 12 × 20.025 = 15 + 240.300 = 255.300
If the Square Root of 401 is 20.025. Find the Value of the Square Root of 4.01.
Let us represent √4.01 in p/q form i.e. √(401/100) = 4.01/10 = 2.002. Hence, the value of √4.01 = 2.002
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