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Square Root of 172

The square root of 172 is expressed as √172 in the radical form and as (172)½ or (172)0.5 in the exponent form. The square root of 172 rounded up to 6 decimal places is 13.114877. It is the positive solution of the equation x2 = 172. We can express the square root of 172 in its lowest radical form as 2 √43.

  • Square Root of 172: 13.114877048604
  • Square Root of 172 in exponential form: (172)½ or (172)0.5
  • Square Root of 172 in radical form: √172 or 2 √43

Square Root of 172

1. What is the Square Root of 172?
2. How to find the Square Root of 172?
3. Is the Square Root of 172 Irrational?
4. FAQs

What is the Square Root of 172?

The square root of 172, (or root 172), is the number which when multiplied by itself gives the product as 172. Therefore, the square root of 172 = √172 = 2 √43 = 13.114877048604.

☛ Check: Square Root Calculator

How to Find Square Root of 172?

Square Root of 172 by Long Division Method

Value of √172 by Long Division Method

Explanation:

  • Forming pairs: 01 and 72
  • Find a number Y (1) such that whose square is <= 1. Now divide 01 by 1 with quotient as 1.
  • Bring down the next pair 72, to the right of the remainder 0. The new dividend is now 72.
  • 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 3) such that 2Z × Z <= 72. After finding Z, together 2 and Z (3) form a new divisor 23 for the new dividend 72.
  • Divide 72 by 23 with the quotient as 3, giving the remainder = 72 - 23 × 3 = 72 - 69 = 3.
  • Now, let's find the decimal places after the quotient 13.
  • 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. 3 + 23 = 26. To the right of 26, find a digit Z (which is 1) such that 26Z × Z <= 300. Together they form a new divisor (261) for the new dividend (300).
  • Divide 300 by 261 with the quotient as 1, giving the remainder = 300 - 261 × 1 = 300 - 261 = 39.
  • Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 172.

Therefore, the square root of 172 by long division method is 13.1 approximately.

Is Square Root of 172 Irrational?

The actual value of √172 is undetermined. The value of √172 up to 25 decimal places is 13.11487704860400130468822. Hence, the square root of 172 is an irrational number.

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Square Root of 172 Solved Examples

  1. Example 1: Solve the equation x2 − 172 = 0

    Solution:

    x2 - 172 = 0 i.e. x2 = 172
    x = ±√172
    Since the value of the square root of 172 is 13.115,
    ⇒ x = +√172 or -√172 = 13.115 or -13.115.

  2. Example 2: If the area of an equilateral triangle is 172√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 = 172√3 in2
    ⇒ a = ±√688 in
    Since length can't be negative,
    ⇒ a = √688 = 2 √172
    We know that the square root of 172 is 13.115.
    ⇒ a = 26.230 in

  3. Example 3: If the area of a square is 172 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 = 172 in2
    ⇒ a = ±√172 in
    Since length can't be negative,
    ⇒ a = √172 = 13.115 in

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FAQs on the Square Root of 172

What is the Value of the Square Root of 172?

The square root of 172 is 13.11487.

Why is the Square Root of 172 an Irrational Number?

Upon prime factorizing 172 i.e. 22 × 431, 43 is in odd power. Therefore, the square root of 172 is irrational.

What is the Square of the Square Root of 172?

The square of the square root of 172 is the number 172 itself i.e. (√172)2 = (172)2/2 = 172.

Evaluate 16 plus 13 square root 172

The given expression is 16 + 13 √172. We know that the square root of 172 is 13.115. Therefore, 16 + 13 √172 = 16 + 13 × 13.115 = 16 + 170.493 = 186.493

Is the number 172 a Perfect Square?

The prime factorization of 172 = 22 × 431. Here, the prime factor 43 is not in the pair. Therefore, 172 is not a perfect square.

What is the Square Root of 172 in Simplest Radical Form?

We need to express 172 as the product of its prime factors i.e. 172 = 2 × 2 × 43. Therefore, √172 = √2 × 2 × 43 = 2 √43. Thus, the square root of 172 in the lowest radical form is 2 √43.

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