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Square Root of 147

The Square Root of 147 is a number which when multiplied by itself, results in the number 147. The square root is an integral part of math that everyone must learn. We will learn how to calculate the Square Root of 147 and look at a few problems to help us understand this topic.

Square Root of 147: √147 = 12.12435565...
Square of 147: 147² = 21,609

1. What is the Square Root of 147?
2. Is Square Root of 147 Rational or Irrational?
3. How to Find the Square Root of 147?
4. Important Notes
5. FAQs on Square Root of 147

What is the square root of 147?

The square root of a number n is written as √n. This number when squared or multiplied by itself results in the original number n. The square root of 147 can be written in multiple ways

  • Radical form: √147 = 7√3 
  • Decimal form: 12.124
  • Exponent form: (147)1/2

Is Square Root of 147 Rational or Irrational?

  • 147 is a number that is not a perfect square, meaning it does not have a natural number as its square root.
  • Also, its square root cannot be expressed as a fraction of the form p/q which tells us that the square root of 147 is an irrational number.

How to Find the Square Root of 147?

There are 2 ways to find the square root of 147-

  • Long Division Method
  • Prime Factorization

One can find out other methods by clicking here

Long Division Method

The square root of 147 by long division method consists of the following steps:

  • Step 1: Starting from the right, we will pair up the digits 147 by putting a bar above 47 and 1 separately. We also pair the 0s in decimals in pairs of 2 from left to right.
  • Step 2: Find a number that, when multiplied by itself, gives a product less than or equal to 1. This will be 1 obviously, so place 1 in the quotient and the divisors place which will result in the remainder being 0. 
  • Step 3: Drag down 47 beside the remainder 0. Also, add the divisor to itself and write it below.(1+1=2)
  • Step 3:  Find a number X such that 2X × X results in a number less than or equal to 47. The number 2 fits here so fill it next to 2 in the divisor as well as next to 1 in the quotient. 
  • Step 4: Find the remainder and now drag down the pair of 0s from the decimal part of the number. Adding, X to the divisor, the new divisor becomes 24. 
  • Step 5: Repeat this process to get the decimal places you want.

Square Root of 147

Therefore, the square root of 147 = 12.124

Prime Factorization

  • To find the square root of 147, we shall first express it in terms of its prime factors.
    147 = 3 × 7 × 7 
  • Next, this can be reduced further to
    147 = 72 × 3
  • Finally, to find the root of this from here it is very easy,
    √147 = √(72 × 3)
    √147 = 7√3 = 12.124

Therefore, the Square Root of 147 ≅ 12.124

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Important Notes

  • There exists a positive and negative root of 147, 12.124 and -12.124
  • There will be n/2 digits in the square root of an even number with n digits.
  • There will be (n+2)/2 digits in the square root of an odd number with n digits.
 

Solved Examples

  1. Example 1: Mike wants to cover his room's floor with tiles. The floor is square-shaped and it has an area of 147 square feet. What will be the length of the room's floor? Round your answer to the nearest tenth.

    Solution:

    Let us assume that the length of the room is x feet. Then the area of the room's floor is x2 square feet. By the given information:
    x2 = 147
    x = √147 = 12.124 feet.
    Hence, the length of the room is 12.1 feet.

  2. Example 2: Joel knew that 12.124 is a square root of 147. He wanted to know if -12.124 is also a square root of 147? Can you clarify his doubt?

    Solution: 

    Let us take an example of a perfect square number and extend the same logic to clarify her doubt. We know that 6 is a square root of 36 because 6 multiplied by itself gives 36
    But what about -6? Let us multiply and check.
    -6 × -6 = 36, because (- × - = +). Therefore -6 is also a square root of 36.
    Going by the same logic, -12.124 is also the square root of 147.

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FAQs on Square Root of 147

What is the prime factorization of 147?

Prime factorization of 147: 72 × 3 = 7√3 = 12.124.

Is 147 a perfect square root?

147 is not a perfect square. 147 is a natural number, but since there is no other natural number that can be squared to result in the number 147, it is NOT a perfect square.

What is the square root of 147 in the simplest radical form?

7√3 is the simplest radical form.

Is the square root of 147 a rational number?

No, the square root of 147 is not a rational number since the square root of 147 is non-terminating and cannot be represented in the form of p/q.

Can we find the square root of 147 by the repeated subtraction method?

No, we can’t find the square root of 147 by repeated subtraction method as it can be used only for perfect squares. 

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