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Square Root of 170

The square root of 170 is expressed as √170 in the radical form and as (170)½ or (170)0.5 in the exponent form. The square root of 170 rounded up to 6 decimal places is 13.038405. It is the positive solution of the equation x2 = 170.

  • Square Root of 170: 13.038404810405298
  • Square Root of 170 in exponential form: (170)½ or (170)0.5
  • Square Root of 170 in radical form: √170
1. What Is the Square Root of 170?
2. Is Square Root of 170 Rational or Irrational?
3. How to Find the Square Root of 170?
4. FAQs on Square Root of 170

What Is the Square Root of 170?

  • If a = b2, then √a = b, where a and b are natural numbers. √a is the square root of a and it is expressed in the exponential form as a½ .
  • √170 = √(a number × a number). 
  • √170 = (13.038 × 13.038) or (- 13.038 × -3.038) ⇒ √170 = ±13.038.

Is Square Root of 170 Rational or Irrational?

Irrational numbers are the real numbers that cannot be expressed as the ratio of two integers. As √170 = 13.0384048104053, hence the square root of 170 is an irrational number where the numbers after the decimal point go up to infinity.

Tips and Tricks

  • The square root of 170 is closer to the perfect square 169. Therefore, we can easily evaluate the approximate value of √170.
  • 1 is the least number to be subtracted and 19 is the least number to be added to make it a perfect square. (170 - 1 = 169) and (170 + 19 = 189).

How to Find the Square Root of 170?

The square root of 170 or any number can be calculated in many ways. Two of them are the prime factorization method and the long division method.

Square Root of 170 in its Simplest Radical Form

The square root of 170 is expressed in the radical form as √170. This can be simplified using the prime factorization. Let us express 170 as a product of its prime factors. 170 = 2 ×  5 × 17. As each of them doesn't have a pair factor, they cannot be simplified further. Thus, √170 cannot be simplified. However, while working on evaluation and simplifications, we can express √170 = √(2 ×  5 × 17). 

Square Root of 170 by the Long Division Method

The long division method helps us to find a more accurate value of square root of any number. The following are the steps to evaluate the square root of 170 by the long division method.

  • Step 1: Write 170.000000. Take the number in pairs from the right. 1 stands alone. Now divide 1 by a number such that (number × number) gives  ≤ 1.
  • Obtain quotient = 1 and remainder = 0. Double the quotient. We get 2. Have 70 as our new divisor. Bring down 70 for division.
  • Step 2: Find a number such that (20 + that number) × that number gives the product ≤ 70.  We find that 23 × 3 = 69. Subtract from 70 and get 1 as the remainder. Bring down the pair of zeros. 100 is our new divisor. 13 is our quotient and on doubling it becomes 26 and 260 is our new divisor. Find a number such that (260 + the number) × number gets 100 or less than that. We cannot find such a number. Hence (260 + 0) ×0 = 0. Subtract and get 100 as the remainder and bring down the zeros. 1 00 00 becomes the new dividend.
  • Step 3: Double the quotient. 130 × 2 = 260. Have 2600  in the place of the new divisor. Find a number such that (2600 + that number) × number ≤ 1 00 00. We find 2603 × 3 = 78 09. Subtract this from 1 00 00 and get the remainder as 21 91.

Repeat the steps until we approximate the square root to 3 decimal places. √170 =  13.038

square root of 170 by Division Method

Explore Square roots using illustrations and interactive examples: 

Important Notes

  • The square root of 170 is 13.038 approximated to 3 decimal places.
  • The simplified form of 170 in its radical form is √170.
  • √170 is an irrational number.
 

Square Root of 170 Solved Examples

  1. Example 1: If a ladder is placed one foot away from the wall and the ladder reaches the top of the wall at 13 feet, find the ladder's length.

    Solution:

    This forms a right angle and we apply the Pythagorean theorem.
    (The distance of the ladder from the wall)2 + (The height of the ladder)2 = (The length of the ladder)2
    12 + 132 = length of the ladder2 
    1 + 169 = length of the ladder2 = 170
    length of the ladder = √170.
    Thus, the length of the ladder = 13.04 feet.​​​​​​

  2. Example 2: Mike's rectangular field has length as twice as its width. If the area of the field is 340 sq.yards, find the perimeter of the field.

    Solution: 

    The area of the field = length × breadth sq yards.
    If the length of the field is l yards, then the width is 2l  yards.
    Therefore, area of the field = l × 2l  = 2 l2 sq yards and perimeter = 6l yards.
    2 l2  = 340
    l2 = 340 ÷ 2 = 170
    l = √170
    l = 13. 038 yards and width = 2l = 2 × 13.038 = 26.076 yards.
    Perimeter = 6l = 6 × 13.038 = 78.228 yards.
    Thus, the perimeter of field = 78.228 yards.

  3. Example: If the surface area of a sphere is 680π in2. Find the radius of the sphere.

    Solution:

    Let 'r' be the radius of the sphere.
    ⇒ Area of the sphere = 4πr2 = 680π in2
    ⇒ r = ±√170 in
    Since radius can't be negative,
    ⇒ r = √170
    The square root of 170 is 13.038.
    ⇒ r = 13.038 in

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FAQs on the Square Root of 170

What is the Value of the Square Root of 170?

The square root of 170 is 13.0384.

Why is the Square Root of 170 an Irrational Number?

Upon prime factorizing 170 i.e. 21 × 51 × 171, 2 is in odd power. Therefore, the square root of 170 is irrational.

What is the Value of 11 square root 170?

The square root of 170 is 13.038. Therefore, 11 √170 = 11 × 13.038 = 143.422.

Evaluate 2 plus 9 square root 170

The given expression is 2 + 9 √170. We know that the square root of 170 is 13.038. Therefore, 2 + 9 √170 = 2 + 9 × 13.038 = 2 + 117.346 = 119.346

Is the number 170 a Perfect Square?

The prime factorization of 170 = 21 × 51 × 171. Here, the prime factor 2 is not in the pair. Therefore, 170 is not a perfect square.

If the Square Root of 170 is 13.038. Find the Value of the Square Root of 1.7.

Let us represent √1.7 in p/q form i.e. √(170/100) = 1.7/10 = 1.304. Hence, the value of √1.7 = 1.304

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