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Square Root of 292

The square root of 292 is expressed as √292 in the radical form and as (292)½ or (292)0.5 in the exponent form. The square root of 292 rounded up to 8 decimal places is 17.08800749. It is the positive solution of the equation x2 = 292. We can express the square root of 292 in its lowest radical form as 2 √73.

  • Square Root of 292: 17.08800749063506
  • Square Root of 292 in exponential form: (292)½ or (292)0.5
  • Square Root of 292 in radical form: √292 or 2 √73

Square Root of 292

1. What is the Square Root of 292?
2. How to find the Square Root of 292?
3. Is the Square Root of 292 Irrational?
4. FAQs

What is the Square Root of 292?

The square root of 292, (or root 292), is the number which when multiplied by itself gives the product as 292. Therefore, the square root of 292 = √292 = 2 √73 = 17.08800749063506.

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How to Find Square Root of 292?

Square Root of 292 by Long Division Method

Value of √292 by Long Division Method

Explanation:

  • Forming pairs: 02 and 92
  • 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 92, to the right of the remainder 1. The new dividend is now 192.
  • 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 <= 192. After finding Z, together 2 and Z (7) form a new divisor 27 for the new dividend 192.
  • Divide 192 by 27 with the quotient as 7, giving the remainder = 192 - 27 × 7 = 192 - 189 = 3.
  • Now, let's find the decimal places after the quotient 17.
  • 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. 7 + 27 = 34. To the right of 34, find a digit Z (which is 0) such that 34Z × Z <= 300. Together they form a new divisor (340) for the new dividend (300).
  • Divide 300 by 340 with the quotient as 0, giving the remainder = 300 - 340 × 0 = 300 - 0 = 300.
  • Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 292.

Therefore, the square root of 292 by long division method is 17.0 approx.

Is Square Root of 292 Irrational?

The actual value of √292 is undetermined. The value of √292 up to 25 decimal places is 17.08800749063506233574330. Hence, the square root of 292 is an irrational number.

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Square Root of 292 Solved Examples

  1. Example 1: Solve the equation x2 − 292 = 0

    Solution:

    x2 - 292 = 0 i.e. x2 = 292
    x = ±√292
    Since the value of the square root of 292 is 17.088,
    ⇒ x = +√292 or -√292 = 17.088 or -17.088.

  2. Example 2: If the area of a square is 292 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 = 292 in2
    ⇒ a = ±√292 in
    Since length can't be negative,
    ⇒ a = √292 = 17.088 in

  3. Example 3: If the area of a circle is 292π in2. Find the radius of the circle.

    Solution:

    Let 'r' be the radius of the circle.
    ⇒ Area of the circle = πr2 = 292π in2
    ⇒ r = ±√292 in
    Since radius can't be negative,
    ⇒ r = √292
    The square root of 292 is 17.088.
    ⇒ r = 17.088 in

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FAQs on the Square Root of 292

What is the Value of the Square Root of 292?

The square root of 292 is 17.088.

Why is the Square Root of 292 an Irrational Number?

Upon prime factorizing 292 i.e. 22 × 731, 73 is in odd power. Therefore, the square root of 292 is irrational.

What is the Value of 18 square root 292?

The square root of 292 is 17.088. Therefore, 18 √292 = 18 × 17.088 = 307.584.

What is the Square of the Square Root of 292?

The square of the square root of 292 is the number 292 itself i.e. (√292)2 = (292)2/2 = 292.

What is the Square Root of 292 in Simplest Radical Form?

We need to express 292 as the product of its prime factors i.e. 292 = 2 × 2 × 73. Therefore, √292 = √2 × 2 × 73 = 2 √73. Thus, the square root of 292 in the lowest radical form is 2 √73.

Evaluate 18 plus 14 square root 292

The given expression is 18 + 14 √292. We know that the square root of 292 is 17.088. Therefore, 18 + 14 √292 = 18 + 14 × 17.088 = 18 + 239.232 = 257.232

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