Square Root of 464
The square root of 464 is expressed as √464 in the radical form and as (464)½ or (464)0.5 in the exponent form. The square root of 464 rounded up to 6 decimal places is 21.540659. It is the positive solution of the equation x2 = 464. We can express the square root of 464 in its lowest radical form as 4 √29.
- Square Root of 464: 21.540659228538015
- Square Root of 464 in exponential form: (464)½ or (464)0.5
- Square Root of 464 in radical form: √464 or 4 √29
1. | What is the Square Root of 464? |
2. | How to find the Square Root of 464? |
3. | Is the Square Root of 464 Irrational? |
4. | FAQs |
What is the Square Root of 464?
The square root of 464, (or root 464), is the number which when multiplied by itself gives the product as 464. Therefore, the square root of 464 = √464 = 4 √29 = 21.540659228538015.
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How to Find Square Root of 464?
Value of √464 by Long Division Method
Explanation:
- Forming pairs: 04 and 64
- 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 64, to the right of the remainder 0. The new dividend is now 64.
- 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 1) such that 4Z × Z <= 64. After finding Z, together 4 and Z (1) form a new divisor 41 for the new dividend 64.
- Divide 64 by 41 with the quotient as 1, giving the remainder = 64 - 41 × 1 = 64 - 41 = 23.
- Now, let's find the decimal places after the quotient 21.
- Bring down 00 to the right of this remainder 23. The new dividend is now 2300.
- Add the last digit of quotient to divisor i.e. 1 + 41 = 42. To the right of 42, find a digit Z (which is 5) such that 42Z × Z <= 2300. Together they form a new divisor (425) for the new dividend (2300).
- Divide 2300 by 425 with the quotient as 5, giving the remainder = 2300 - 425 × 5 = 2300 - 2125 = 175.
- Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 464.
Therefore, the square root of 464 by long division method is 21.5 approx.
Is Square Root of 464 Irrational?
The actual value of √464 is undetermined. The value of √464 up to 25 decimal places is 21.54065922853801612500284. Hence, the square root of 464 is an irrational number.
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- Square Root of 1024 - √1024 = 32
- Square Root of 76 - √76 = 8.71780
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Square Root of 464 Solved Examples
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Example 1: Solve the equation x2 − 464 = 0
Solution:
x2 - 464 = 0 i.e. x2 = 464
x = ±√464
Since the value of the square root of 464 is 21.541,
⇒ x = +√464 or -√464 = 21.541 or -21.541. -
Example 2: If the area of an equilateral triangle is 464√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 = 464√3 in2
⇒ a = ±√1856 in
Since length can't be negative,
⇒ a = √1856 = 2 √464
We know that the square root of 464 is 21.541.
⇒ a = 43.081 in -
Example 3: If the area of a square is 464 in2. Find the length of the side of the square.
Solution:
Let 'a' be the length of the side of the square.
⇒ Area of the square = a2 = 464 in2
⇒ a = ±√464 in
Since length can't be negative,
⇒ a = √464 = 21.541 in
FAQs on the Square Root of 464
What is the Value of the Square Root of 464?
The square root of 464 is 21.54065.
Why is the Square Root of 464 an Irrational Number?
Upon prime factorizing 464 i.e. 24 × 291, 29 is in odd power. Therefore, the square root of 464 is irrational.
What is the Square of the Square Root of 464?
The square of the square root of 464 is the number 464 itself i.e. (√464)2 = (464)2/2 = 464.
If the Square Root of 464 is 21.541. Find the Value of the Square Root of 4.64.
Let us represent √4.64 in p/q form i.e. √(464/100) = 4.64/10 = 2.154. Hence, the value of √4.64 = 2.154
Is the number 464 a Perfect Square?
The prime factorization of 464 = 24 × 291. Here, the prime factor 29 is not in the pair. Therefore, 464 is not a perfect square.
What is the Value of 11 square root 464?
The square root of 464 is 21.541. Therefore, 11 √464 = 11 × 21.541 = 236.947.
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