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
|1.||What Is the Square Root of 15?|
|2.||Is Square Root of 15 Rational or Irrational?|
|3.||How to Find the Square Root of 15?|
|4.||FAQs on Square Root of 15|
What Is the Square Root of 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.
Is the Square Root of 15 Rational or Irrational?
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.
How to Find the Square Root of 15?
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)
- 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
- 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 15½. 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)
Square Root of 15 Solved Examples
Example 1: Mr. Johnson wants to fence his square garden. The garden has an area of 15 square feet. How long is each side of the garden? Round your answer to three decimals.
We know that the area of a square is side × side. If we take the length of the garden as x, then x × x = 15
We can easily find out the value of x using the concept of the square root. The square root of 15 is √15 approx 3.872 (rounded to three decimals).
So, the side length of the garden is approx 3.872 feet.
Example 2: Mathew has a carrom board of area 15 sq. units. He measured the length of the carrom board to be 3.872 units. Why is that so?
We know that the area of a square is side × side. The length of the square carrom board is 3.872, this means 3.872 x 3.872 = 14.99 sq. units and the nearest whole number is 15. By finding the square root of the area of 15 sq. units, we can find the side length of the carrom board.
Side of the square board = √15= 3.872.
So, the side length of the carrom board is 3.872 units.
Example: If the area of a square is 15 in2. Find the length of the side of the square.
Let 'a' be the length of the side of the square.
⇒ Area of the square = a2 = 15 in2
⇒ a = ±√15 in
Since length can't be negative,
⇒ a = √15 = 3.873 in
FAQs on the Square Root of 15
What is the Value of the Square Root of 15?
The square root of 15 is 3.87298.
Why is the Square Root of 15 an Irrational Number?
Upon prime factorizing 15 i.e. 31 × 51, 3 is in odd power. Therefore, the square root of 15 is irrational.
What is the Value of 5 square root 15?
The square root of 15 is 3.873. Therefore, 5 √15 = 5 × 3.873 = 19.365.
What is the Square of the Square Root of 15?
The square of the square root of 15 is the number 15 itself i.e. (√15)2 = (15)2/2 = 15.
What is the Square Root of 15 in Simplest Radical Form?
We need to express 15 as the product of its prime factors i.e. 15 = 3 × 5. Therefore, as visible, the radical form of the square root of 15 cannot be simplified further. Therefore, the simplest radical form of the square root of 15 can be written as √15
What is the Square Root of -15?
The square root of -15 is an imaginary number. It can be written as √-15 = √-1 × √15 = i √15 = 3.872i
where i = √-1 and it is called the imaginary unit.