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Square Root of 364

The square root of 364 is expressed as √364 in the radical form and as (364)½ or (364)0.5 in the exponent form. The square root of 364 rounded up to 8 decimal places is 19.07878403. It is the positive solution of the equation x2 = 364. We can express the square root of 364 in its lowest radical form as 2 √91.

  • Square Root of 364: 19.078784028338912
  • Square Root of 364 in exponential form: (364)½ or (364)0.5
  • Square Root of 364 in radical form: √364 or 2 √91

Square Root of 364

1. What is the Square Root of 364?
2. How to find the Square Root of 364?
3. Is the Square Root of 364 Irrational?
4. FAQs

What is the Square Root of 364?

The square root of 364, (or root 364), is the number which when multiplied by itself gives the product as 364. Therefore, the square root of 364 = √364 = 2 √91 = 19.078784028338912.

☛ Check: Square Root Calculator

How to Find Square Root of 364?

Square Root of 364 by Long Division Method

Value of √364 by Long Division Method

Explanation:

  • Forming pairs: 03 and 64
  • Find a number Y (1) such that whose square is <= 3. Now divide 03 by 1 with quotient as 1.
  • Bring down the next pair 64, to the right of the remainder 2. The new dividend is now 264.
  • Add the last digit of the quotient (1) to the divisor (1) i.e. 1 + 1 = 2. To the right of 2, find a digit Z (which is 9) such that 2Z × Z <= 264. After finding Z, together 2 and Z (9) form a new divisor 29 for the new dividend 264.
  • Divide 264 by 29 with the quotient as 9, giving the remainder = 264 - 29 × 9 = 264 - 261 = 3.
  • Now, let's find the decimal places after the quotient 19.
  • Bring down 00 to the right of this remainder 3. The new dividend is now 300.
  • Add the last digit of quotient to divisor i.e. 9 + 29 = 38. To the right of 38, find a digit Z (which is 0) such that 38Z × Z <= 300. Together they form a new divisor (380) for the new dividend (300).
  • Divide 300 by 380 with the quotient as 0, giving the remainder = 300 - 380 × 0 = 300 - 0 = 300.
  • Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 364.

Therefore, the square root of 364 by long division method is 19.0 approximately.

Is Square Root of 364 Irrational?

The actual value of √364 is undetermined. The value of √364 up to 25 decimal places is 19.07878402833891298305243. Hence, the square root of 364 is an irrational number.

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Square Root of 364 Solved Examples

  1. Example 1: Solve the equation x2 − 364 = 0

    Solution:

    x2 - 364 = 0 i.e. x2 = 364
    x = ±√364
    Since the value of the square root of 364 is 19.079,
    ⇒ x = +√364 or -√364 = 19.079 or -19.079.

  2. Example 2: If the area of a circle is 364π in2. Find the radius of the circle.

    Solution:

    Let 'r' be the radius of the circle.
    ⇒ Area of the circle = πr2 = 364π in2
    ⇒ r = ±√364 in
    Since radius can't be negative,
    ⇒ r = √364
    The square root of 364 is 19.079.
    ⇒ r = 19.079 in

  3. Example 3: If the surface area of a sphere is 1456π in2. Find the radius of the sphere.

    Solution:

    Let 'r' be the radius of the sphere.
    ⇒ Area of the sphere = 4πr2 = 1456π in2
    ⇒ r = ±√364 in
    Since radius can't be negative,
    ⇒ r = √364
    The square root of 364 is 19.079.
    ⇒ r = 19.079 in

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FAQs on the Square Root of 364

What is the Value of the Square Root of 364?

The square root of 364 is 19.07878.

Why is the Square Root of 364 an Irrational Number?

Upon prime factorizing 364 i.e. 22 × 71 × 131, 7 is in odd power. Therefore, the square root of 364 is irrational.

Evaluate 16 plus 16 square root 364

The given expression is 16 + 16 √364. We know that the square root of 364 is 19.079. Therefore, 16 + 16 √364 = 16 + 16 × 19.079 = 16 + 305.261 = 321.261

Is the number 364 a Perfect Square?

The prime factorization of 364 = 22 × 71 × 131. Here, the prime factor 7 is not in the pair. Therefore, 364 is not a perfect square.

What is the Square of the Square Root of 364?

The square of the square root of 364 is the number 364 itself i.e. (√364)2 = (364)2/2 = 364.

If the Square Root of 364 is 19.079. Find the Value of the Square Root of 3.64.

Let us represent √3.64 in p/q form i.e. √(364/100) = 3.64/10 = 1.908. Hence, the value of √3.64 = 1.908

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