Square Root of 15

The square root of 15 is expressed as √15 in the radical form and as (15)^½ or (15)^0.5 in the exponent form. The square root of 15 rounded up to 8 decimal places is 3.87298335. It is the positive solution of the equation x² = 15.

• Square Root of 15: 3.872983346207417
• Square Root of 15 in exponential form: (15)^½ or (15)^0.5
• Square Root of 15 in radical form: √15

We know that addition has an inverse operation as subtraction and multiplication has an inverse operation as division. Similarly, finding the square root is an inverse operation of squaring. The square root of 15 is the number that gets multiplied to itself to give the number 15. So, we have to think of a number whose square is 15 By trial and error method, we can see that, there does not exist any integer whose square is 15 But we can find the square root of 15 using the calculator and we get, √15 approx 3.872983... We can check this answer and we surely are going to need a calculator here, 3.872983 × 3.872983...approx 14.999997318289... Phew! That's quite close to 15.

The square root of 15 is not a rational number. It is an irrational number. Here's why. A rational number is a number that can be expressed in the form of p/q, where p, q ∈ Z and q ≠ 0. A number is irrational if it is non-terminating with no repeating patterns in its decimal part. Now let us look at the square root of 15, the decimal representation of √15 is 3.87298334621... Do you think the decimal part stops after 3.87298334621...? No, it is never-ending. It is a non-terminating decimal with non-repeating digits. The number 2.15215427125... can't be written in p/q form, where p and q are integers. So, the square root of 15 is not a rational number. It is an irrational number.

We will discuss two methods of finding the square root of 15. Express the radicand to be the product involving perfect square(s) and simplifying it
Long division method for perfect and non-perfect squares. Let's discuss the first method, Simplifying a square root means to rewrite it in such a way that there are no perfect squares left in the radicand. √50 can be simplified to 5√2 but √15 cannot be simplified further. Let us learn the reason behind. The prime factorization of 15 is 15 = 3 × 5. For simplifying √15 further we will need one or more pairs of the same factors. Such pairs of factors are not available. Therefore, √15 cannot be simplified further.

Square Root of 15 By Long Division

The value of the square root of 15 by long division is found using the following steps:

• Step 1: Starting from the right, we will pair up the digits by putting a bar above them.
• Step 2: Find a number that, when multiplied to itself, gives the product less than or equal to 15 and close to 15. So, the number is 3. Putting the divisor as 3, we get the quotient as 3 (same as the divisor), we get the remainder to be 6 
• Step 3: Double the divisor and enter it with a blank on its right. Guess the largest possible digit to fill in the blank which will become the new digit in the quotient, such that when the new divisor is multiplied to the new quotient the resultant product is less than or equal to the dividend. Divide and write the remainder. Repeat this process to get the decimal places until you want. 

The square root of 15 by long division method = 3.872 (to three decimal places)

Similarly,

• The square root of 20 = 4.472 (to three decimals)
• The square root of 25 = 5
• The square root of 16 = 4
• The square root of 14 = 3.741 (to three decimals) 

25 and 16 are perfect squares since their square roots are integers.

Explore Square roots using illustrations and interactive examples

• Square Root of 25
• Square Root of 30
• Square Root of 5
• Square Root of 250
• Square Root of 65

• Jenny has a square table that has an area of 15 square inches. She covered it with a table cloth of area 25 square inches. How many inches does the cloth hang around the table on each side?

• The square root is the inverse operation of squaring.
• The square root of 15 can be expressed as √15 or 15^½. It is an irrational number.
• We can find the square root of 15 using the long division method. The square root of 15 by long division method = 3.872 (to three decimal places)