Square Root of 145
The square root of 145 is the inverse of the mathematical operation of the square of the number whose square is 145. The number 145 has two distinct prime factors 5 and 29. We will now calculate the value of the square root of 145 using the long division method and the approximation method. Also, we will look at some interesting problems and facts.
- Square root of 145: 12.0415
- Square of 145: 21025
|1.||What Is the Square Root of 145?|
|2.||Is Square Root of 145 Rational or Irrational?|
|3.||How to Find the Square Root of 145?|
|4.||FAQs on Square Root of 145|
|5.||Important Notes on Square Root of 145|
What Is the Square Root of 145?
- The square root of 145 in decimal form is 12.0415
- The square root of 145 is represented as √145 in radical form.
- The square root of 145 is represented as (145)1/2 in exponential form.
Is Square Root of 145 Rational or Irrational?
The square root of 145 is a non-terminating and non-repeating number.
Hence, it cannot be represented in the form of p/q where q ≠ 0.
Therefore, the square root of 145 is an irrational number.
How to Find the Square Root of 145?
We will now find the square root of 145 using the methods given below:
Square Root of 145 Using Approximation Method
- First, we will find the two consecutive numbers such that 145 lies between their perfect squares.
In this case, the numbers are 12 (144) and 13 (169).
So, the whole number part of the square root of 145 is 12.
- Now, for the decimal part we will use the below formula:
(Given number - Smaller perfect square) / (Greater perfect square - smaller perfect square)
= (145 - 144)/(169 - 144) = 1/25 = 0.04
- Hence, the approx. value of the square root of 145 by the approximation method is 12.04
Square Root of 145 by Long Division
Now we will calculate the square root of 145 by the long division method.
- Start pairing the digits from the right side of the number 145 by putting a bar on top of them. Here we will have two pairs, 45 and 1 (pairing from right).
- Now, find a number (a) whose square is ≤ 1. The value of a will be 1 as 1 × 1 = 1≤ 1.
- We get the quotient (1). Now, we will add the divisor a with itself and get the new divisor 2a (2).
- Drag the next pair down (new dividend becomes 045) and find a number (A) such that 2A × A ≤ 45. In this case, the value of A will be 2.
- Now, put a decimal in the dividend (145) after 5 and quotient (12) after 2 simultaneously. Also, add 3 pairs of zero in the dividend after the decimal (145. 00 00 00) and repeat the above step for the remaining three pairs of zero.
So, we get the value of the square root of √145 = 12.041 by the long division method.
Explore square roots using illustrations and interactive examples.
- The square root of 145 is an irrational number.
- The number 145 is not a perfect square.
- The square root of -145 is an imaginary number.
Square Root of 145 Solved Examples
Example 1: What is the square root of -√145?
The square root of negative numbers is represented by imaginary numbers.
The square root of -√145 is written as √145 i. Where (i = -√1)
Example 2: Martin wants to find the value of (10√29/√145/). Can you help Martin?
We know that √145= √29 × √5
And 10 = √10 × √10
Also, √10 = √5 × √2
Therefore, 10 = √5 × √5 × √2 × √2
Now (10√29/√145) = (√5 × √5 × √2 × √2 × √29) / (√29 × √5)
= √5 × √2 × √2
FAQs on Square Roots of 145
What is the square of 145?
The square of 145 is (145)2 = 21025.
What is the negative square root of 145?
The negative square root of 145 is -12.041
What is the prime factorization of 145?
The prime factorization of 145 is: 5 × 29
Can we calculate the square root of 145 using the prime factorization method?
No, we cannot find the square root of 145 using the prime factorization method.
Because the prime factors of 145 are 5 and 29. Also, the power of 5 and 29 in the prime factorization of 145 is 1.
So, 145 cannot be reduced further.
Is the number 145 a perfect square?
No, 145 is not a perfect square
Because the square root of 145 is a non-terminating and non-repeating number.