The square root of 169 is 13 .

13

The square root of a number is the number that when multiplied to itself gives the original number as the product. Thus the square root of 169 is +13 or -13. This shows that 169 is a perfect square.

The square root of 169 is 13. Since 13 is a whole number, 169 is a perfect square.

Square Root Table 1-100

Is 169 a perfect square number? A number is a perfect square (or a square number) if its square root is an integer; that is to say, it is the product of an integer with itself. Here, the square root of 169 is 13. Therefore, the square root of 169 is an integer, and as a consequence 169 is a perfect square.

Is 80 a perfect square root? 80 is not a perfect square. 80 is a natural number, but since there is no other natural number that can be squared to result in the number 80, it is NOT a perfect square root.

What Is the Square Root of 400? The square root of a number is the number that when multiplied to itself gives the original number as the product. This shows that 400 is a perfect square.

Informally: When you multiply an integer (a “whole” number, positive, negative or zero) times itself, the resulting product is called a square number, or a perfect square or simply “a square.” So, 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on, are all square numbers.

The number 85 is not a perfect square, so its value can be approximated between 9 and 10. √85 = 9.21. The exact value of the square root of 85 can be calculated using long division. Further, since 85 is not a perfect square, the remainder is never 0 and the division process is concluded after a few steps.

Here are step-by-step instructions for how to get the square root of 85 to the nearest tenth:

1. Step 1: Calculate. We calculate the square root of 85 to be: √85 = 9.21954445729289.
2. Step 2: Reduce. 9.21.
3. Step 3: Round. Round 9.21 so you only have one digit after the decimal point to get the answer: 9.2.

The factors of 85 are 1, 5, 17, and 85.

The square root of 85 cannot be simplified. √85 is already in its simplest radical form. If you are using a computer that has Excel or Numbers, then you can enter SQRT(85) in a cell to get the square root of 85. Below is the result we got with 13 decimals.

List of Perfect Squares

The square root of 73 is expressed as √73 in the radical form and as (73)½ or (73)0.5 in the exponent form. The square root of 73 rounded up to 7 decimal places is 8.5440037….Square Root of 73 in radical form: √73.

9.2

Square Root to the Nearest Tenth

The square root of 60 is expressed as √60 in the radical form and as (60)½ or (60)0.5 in the exponent form….Square Root of 60.

But you can get better and better approximations by: start with a number whose square is close to 85. (9 or 10. 92 is closer, so start there. That answer is accurate to 4 decimal places.

Explanation: 81=9⋅9 then the square root of √81=9 . Because the double multiplication for the same sign is always positive, the square root is also valid with the other sign 81=(−9)⋅(−9) then √81=−9 and we can say that √81=±9 .

4√2

Because 16 is a perfect square, we can pull it out of the square root as a 4. That will simplify down to 4√10 because there are no additional perfect square factors in 10, the resultant is simplified. Therefore √160 simplifies to 4 √10 .

Since 89 is prime, √89 cannot be simplified. You can approximate it using a Newton Raphson method. I like to reformulate it a little as follows: Let n=89 be the number you want the square root of.

Since no factor is repeated, the square root cannot be simplified. It is an irrational number a little larger than 3=√9 .

The square root of 10 is an irrational number with never-ending digits.

Example Square Roots: The 2nd root of 10, or 10 radical 2, or the square root of 10 is written as 2√10=√10=±3.162278.

√14 is already simplified. Using a calculator, √14=3.74165738677 .