The square root of 153 is expressed together √153 in the radical type and as (153)½ or (153)0.5 in the exponent form. The square source of 153 rounded as much as 9 decimal locations is 12.369316877. It is the confident solution that the equation x2 = 153. We can express the square source of 153 in its lowest radical type as 3 √17.

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Square source of 153: 12.36931687685298Square root of 153 in exponential form: (153)½ or (153)0.5Square source of 153 in radical form: √153 or 3 √17
1.What Is the Square source of 153?
2.Is Square source of 153 rational or Irrational?
3.How to discover the Square source of 153?
4.Tips and also Tricks
5.FAQs on Square source of 153
6.Important notes on Square source of 153

What Is the Square source of 153?

The square root of a number is the inverse procedure of squaring a number.


A square that a number y is x2 ⇒ y = x × x. 153 = 12.369 × 12.369√153 = √(12.369 × 12.369)153½ = (12.3692)½ 12.369 = 153½ ⇒ √153 = ±12.369

Is Square root of 153 reasonable or Irrational?


√153 = 12.3693168769. √153 can not be composed in the form of p/q, hence it is an irrational number. The value of the square source of 153 is a decimal number who digits after ~ the point is never-ending or non-terminating. 


How to find the Square root of 153?


The square root of 153 or any kind of number deserve to be calculated in many ways. 2 of them are the approximation method and the long department method.

Square root of 153 by Approximation Method

Take two perfect square number which are simply smaller 보다 153 and just higher than 153. √144 12 Using the average method, divide 153 by 12 or 13Let united state divide by 12 ⇒ 153 ÷ 12 = 12.75Find the average of 12,75 and 12.(12.75 + 12) / 2 = 24.75 ÷ 2 = 12.375√153 ≈ 12.369

Square source of 153 by the Long division Method

The long department method helps united state to find a more accurate value of square root of any type of number. Let"s see just how to find the square root of 153 by the long division method.

Start pairing the digits from the appropriate side that the number 153 by placing a bar on height of them. Right here we will have actually two pairs: 53 and 1 (pairing native right).Now, discover a number(a) who square is ≤ 1. The worth of a will be 1 as 1 × 1 = 1≤ 1.Drag the next pair under (new dividend becomes 053) and also find a number (A) such that 2A × A ≤ 53. In this case, the worth of A will certainly be 2.Now, placed a decimal in the dividend (153) after ~ 3 and quotient (12) ~ 2 simultaneously. Also, add 3 pairs of zero in the dividend ~ the decimal (153. 00 00 00) and repeat the above step for the remaining three pairs of zeros.

So, we obtain the value of the square source of √153 = 12.369 by the long department method.

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Explore square roots using illustrations and interactive examples


Tips and also Tricks


The square root of 153 lies between the square source of 144 and 169. Therefore, 12 Use the average technique then, to evaluate the approximate value of √153.

Important Notes

√153 is 12.369 approximated come 3 decimal places.The simplified form of 153 in the radical form is 3√17.153 is an irrational number.

Example 1: Amy stacks 153 books in such a means that there are as many books in each row together the variety of rows. How many publications will she take the end of the setup or how many books will she add to do such an arrangement?

Solution: She demands to find the the very least number to be added to 153 or subtracted indigenous 153 to do it a perfect square. 153 lies between 144 and 169, which are the perfect squares close to 153.153 - 9 = 144 ⇒ 12 × 12 = 144153 + 16 = 169 ⇒ 13 × 13 = 169If Amy decides to have 12 books arranged in 12 rows, she will need to remove 9 books from the arrangement. If she decides to have actually 13 books arranged in 13 rows, she will need 16 more books to fit into the arrangement.


Example 2: What perfect sqaure number should Martin include to 153 so that the new number derived is likewise a perfect square?

Solution: 153 lies in between 144 and 169, which are the perfect squares closer to 153.Adding 16 come 153,153 + 16 = 169√16 = 4√169 = 1316 is a perfect square number169 is also a perfect square number.


Example 3: What perfect sqaure number should Martin subtract from 153 so that the new number acquired is additionally a perfect square?

Solution: 153 lies between 144 and 169 which space the perfect squares closer come 153.Subtracting 9 from 153,153 - 9 = 144√9 = 3√144 = 129 is a perfect square number144 is also a perfect square number.


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FAQs top top the Square root of 153

What is the value of the Square source of 153?

The square source of 153 is 12.36931.

Why is the Square source of 153 one Irrational Number?

Upon prime factorizing 153 i.e. 32 × 171, 17 is in strange power. Therefore, the square root of 153 is irrational.

Evaluate 6 plus 13 square source 153

The provided expression is 6 + 13 √153. We understand that the square source of 153 is 12.369. Therefore, 6 + 13 √153 = 6 + 13 × 12.369 = 6 + 160.801 = 166.801

What is the worth of 10 square source 153?

The square source of 153 is 12.369. Therefore, 10 √153 = 10 × 12.369 = 123.693.

What is the Square source of 153 in simplest Radical Form?

We should express 153 as the product the its prime factors i.e. 153 = 3 × 3 × 17. Therefore, √153 = √3 × 3 × 17 = 3 √17. Thus, the square source of 153 in the shortest radical kind is 3 √17.

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If the Square root of 153 is 12.369. Uncover the value of the Square root of 1.53.

Let us represent √1.53 in p/q form i.e. √(153/100) = 1.53/10 = 1.237. Hence, the value of √1.53 = 1.237