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Square Root of 296

The square root of 296 is expressed as √296 in the radical form and as (296)½ or (296)0.5 in the exponent form. The square root of 296 rounded up to 8 decimal places is 17.20465053. It is the positive solution of the equation x2 = 296. We can express the square root of 296 in its lowest radical form as 2 √74.

  • Square Root of 296: 17.204650534085253
  • Square Root of 296 in exponential form: (296)½ or (296)0.5
  • Square Root of 296 in radical form: √296 or 2 √74

Square Root of 296

1. What is the Square Root of 296?
2. How to find the Square Root of 296?
3. Is the Square Root of 296 Irrational?
4. FAQs

What is the Square Root of 296?

The square root of 296, (or root 296), is the number which when multiplied by itself gives the product as 296. Therefore, the square root of 296 = √296 = 2 √74 = 17.204650534085253.

☛ Check: Square Root Calculator

How to Find Square Root of 296?

Square Root of 296 by Long Division Method

Value of √296 by Long Division Method

Explanation:

  • Forming pairs: 02 and 96
  • Find a number Y (1) such that whose square is <= 2. Now divide 02 by 1 with quotient as 1.
  • Bring down the next pair 96, to the right of the remainder 1. The new dividend is now 196.
  • 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 7) such that 2Z × Z <= 196. After finding Z, together 2 and Z (7) form a new divisor 27 for the new dividend 196.
  • Divide 196 by 27 with the quotient as 7, giving the remainder = 196 - 27 × 7 = 196 - 189 = 7.
  • Now, let's find the decimal places after the quotient 17.
  • Bring down 00 to the right of this remainder 7. The new dividend is now 700.
  • Add the last digit of quotient to divisor i.e. 7 + 27 = 34. To the right of 34, find a digit Z (which is 2) such that 34Z × Z <= 700. Together they form a new divisor (342) for the new dividend (700).
  • Divide 700 by 342 with the quotient as 2, giving the remainder = 700 - 342 × 2 = 700 - 684 = 16.
  • Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 296.

Therefore, the square root of 296 by long division method is 17.2 approx.

Is Square Root of 296 Irrational?

The actual value of √296 is undetermined. The value of √296 up to 25 decimal places is 17.20465053408525354345895. Hence, the square root of 296 is an irrational number.

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Square Root of 296 Solved Examples

  1. Example 1: Solve the equation x2 − 296 = 0

    Solution:

    x2 - 296 = 0 i.e. x2 = 296
    x = ±√296
    Since the value of the square root of 296 is 17.205,
    ⇒ x = +√296 or -√296 = 17.205 or -17.205.

  2. Example 2: If the area of a square is 296 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 = 296 in2
    ⇒ a = ±√296 in
    Since length can't be negative,
    ⇒ a = √296 = 17.205 in

  3. Example 3: If the area of a circle is 296π in2. Find the radius of the circle.

    Solution:

    Let 'r' be the radius of the circle.
    ⇒ Area of the circle = πr2 = 296π in2
    ⇒ r = ±√296 in
    Since radius can't be negative,
    ⇒ r = √296
    The square root of 296 is 17.205.
    ⇒ r = 17.205 in

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FAQs on the Square Root of 296

What is the Value of the Square Root of 296?

The square root of 296 is 17.20465.

Why is the Square Root of 296 an Irrational Number?

Upon prime factorizing 296 i.e. 23 × 371, 2 is in odd power. Therefore, the square root of 296 is irrational.

Evaluate 14 plus 17 square root 296

The given expression is 14 + 17 √296. We know that the square root of 296 is 17.205. Therefore, 14 + 17 √296 = 14 + 17 × 17.205 = 14 + 292.479 = 306.479

What is the Square Root of -296?

The square root of -296 is an imaginary number. It can be written as √-296 = √-1 × √296 = i √296 = 17.204i
where i = √-1 and it is called the imaginary unit.

What is the Square Root of 296 in Simplest Radical Form?

We need to express 296 as the product of its prime factors i.e. 296 = 2 × 2 × 2 × 37. Therefore, √296 = √2 × 2 × 2 × 37 = 2 √74. Thus, the square root of 296 in the lowest radical form is 2 √74.

If the Square Root of 296 is 17.205. Find the Value of the Square Root of 2.96.

Let us represent √2.96 in p/q form i.e. √(296/100) = 2.96/10 = 1.720. Hence, the value of √2.96 = 1.720

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