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Square Root of 162

The number 162 has only two prime factors, 2 and 3. The square root of 162 will be a number whose product with itself results in 162. The square root of 162 can be positive and negative. Now we will find the square root of 162 using different methods and will also look at a few interesting facts and problems.

  • Square root of 162: 12.7279
  • Square of 162: 26244
1. What Is the Square Root of 162?
2. Is Square Root of 162 Rational or Irrational?
3. How to Find the Square Root of 162?
4. FAQs on Square Root of 162
5. Important Notes on Square Root of 162

What Is the Square Root of 162?

  • The square root of 162 can be written as √162 and (162)1/2
  • The square root of 162 is √162 = 12.7279
  • The number 162 is not a perfect square as its square root is not an integer.

Is Square Root of 162 Rational or Irrational?

The square root of 162 is a non-terminating and non-repeating number.
Hence, the square root of 162 is an irrational number as it cannot be expressed in the form of p/q where q ≠ 0.

How to Find the Square root of 162?

Now we will calculate the square root of 162 using the following methods:

  • Prime Factorization Method
  • Long Division Method 

Square Root of 162 Using Prime Factorization Method

  • The prime factorization of 162: 2 × 34
  • The prime factors of 162 in pairs: 2 × (3 × 3) × (3 × 3)
  • Now, the square root of 162: √162 = √ (2 × (3 × 3)2)
  • So, the square root of 162 = (3 × 3) × √2 = 9√2

Square Root of 162 By Long Division

We will now find the square root of 162 by the long division method with the help of the steps given below.

  • Start Grouping the digits from the unit’s place in pairs of two by putting a bar on top of them. We get two pairs in this case (1 and 62).
  • Find a number(n) which when multiplied with itself n × n ≤ 1. So, n will be 1 as 1 × 1 = 1.
  • Now we get the quotient as 1. Also, we have to add the divisor n with itself to get the new divisor. The new divisor here will be 2.
  • Bring down the pair of 62. So, our new dividend is 62. Now find a number(m) such that 2m × m ≤ 62. The number m will be 2 as 22 × 2 = 44 ≤ 62.
  • Add a decimal in the dividend and quotient part simultaneously. Also, add 3 pairs of zero in the dividend part.
  • Repeat the above step for all the pairs of zero.

So, we get the square root of √162 = 12.727 by the long division method.

Square Root of 162

Explore square roots using illustrations and interactive examples

Important Notes:

  • The number 162 is not a perfect square.
  • The square root of 162 is an irrational number.
  • The square root of -162 is an imaginary number.
 

Square Root of 162 Solved Examples

 

  1. Example 1: Wanda wants to find out the square root of -162. Can you help Wanda?

    Solution:
    The square root of negative numbers is imaginary numbers.
    Because a square of any number (positive or negative) will result in a positive number.
    So, the square of -162 is written as √-162 = ±12.7279i. (where i = √-1)

  2.  

    Example 2: Find the square root of 162 using the repeated subtraction method?

    Solution:

    First, find two consecutive perfect squares between which the number 162 will lie. The two perfect squares are 144 (122) and 169 (132).

    Therefore, the whole number part of the square root of 162 will be 12.

    Now, for the decimal part, we will use the below-mentioned formula:

    (Given number - Smaller perfect square) / (Greater perfect square - smaller perfect square) 

    = (162 - 144)/(169 - 144) = 18/25 = 0.72 

    Hence, the square root of 162 via the approximation method is 12.720

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FAQs on Square Roots of 162

What is the negative square root of 162?

The negative square root of 162 is -12.7279

What is the square of 162?

The square of 162 is (162)2 = 26244

Can we find the square root of 162 using the repeated subtraction method?

No, we can’t find the square root of 162 using the repeated subtraction method.
Because the number 162 is not a perfect square.

Is the square root of 162 is a rational number?

No, the square root of 162 is not a rational number
Because we can’t represent it in the form of p/q where q ≠ 0.

How is the square root of 162 is expressed in exponential and radical form?

  • The square root of 162 is represented as (162)1/2 in exponential form.
  • The square root of 162 is represented as √162 in radical form.
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