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

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**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 |

We recognize that addition has an inverse procedure as subtractivity and multiplication has actually 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 offer the number 15. So, we have to think of a number whose square is 15 By trial and error method, we can watch that, there does not exist any kind of integer whose square is 15 But we have the right to discover the square root of 15 making use of the calculator and also we get, √15 approx 3.872983... We can check this answer and also we surely are going to need a calculator here, 3.872983 × 3.872983...approx 14.999997318289... Phew! That"s fairly cshed 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 develop of p/q, where p, q ∈ Z and q ≠ 0. A number is irrational if it is non-terminating through 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 via non-repeating digits. The number 2.15215427125... can not be written in p/q create, wright here 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 2 approaches of finding the square root of 15. Express the radicand also to be the product entailing perfect square(s) and also simplifying itLong department method for perfect and also non-perfect squares. Let"s talk about the first strategy, Simplifying a square root implies to rewrite it in such a way that tright here are no perfect squares left in the radicand also. √50 have the right to be streamlined to 5√2 but √15 cannot be simplified further. Let us learn the factor behind. **The prime factorization of 15 is 15 = 3 × 5**. For simplifying √15 even more we will certainly require one or even more pairs of the exact same factors. Such pairs of factors are not accessible. Because of this, √15 cannot be streamlined even more.

### Square Root of 15 By Long Division

The value of the square root of 15 by lengthy division is uncovered making use of the adhering to steps:

**Tip 1**: Starting from the ideal, we will pair up the digits by placing a bar over them.

**Tip 2**: Find a number that, as soon as multiplied to itself, offers the product much less than or equal to 15 and also cshed to 15. So, the number is 3. Putting the divisor as 3, we obtain the quotient as 3 (exact same as the divisor), we get the remainder to be 6

**Step 3:**Double the divisor and enter it via a blank on its ideal. Guess the largest feasible digit to fill in the empty which will come to be the new digit in the quotient, such that as soon as the new divisor is multiplied to the new quotient the resultant product is much less than or equal to the dividfinish. Divide and also create the remainder. Repeat this process to acquire the decimal places till you want.

The square root of 15 by long department technique = 3.872 (to three decimal places)

Similarly,

The square root of 20 = 4.472 (to 3 decimals)The square root of 25 = 5The square root of 16 = 4The square root of 14 = 3.741 (to 3 decimals)25 and also 16 are perfect squares given that their square roots are integers.

**Explore Square roots using illustrations and interenergetic examples**

**Think Tank:**

Jenny has actually a square table that has an area of 15 square inches. She covered it through a table fabric of area 25 square inches. How many inches does the towel hang approximately the table on each side?

**Important Notes:**

The square root is the inverse procedure of squaring.The square root of 15 deserve to be expressed as √15 or 15½. It is an irrational number.We can find the square root of 15 using the lengthy division approach. The square root of 15 by lengthy division method = 3.872 (to 3 decimal places)

**Example 2**: Mathew has actually a carrom board of location 15 sq. systems. He measured the length of the carrom board to be 3.872 units. Why is that so?

**Solution**

We know that the location of a square is side × side. The size of the square carrom board is 3.872, this means 3.872 x 3.872 = 14.99 sq. units and also the nearest totality number is 15. By finding the square root of the area of 15 sq. systems, we have the right to uncover the side length of the carrom board.Side of the square board = √15= 3.872.So, the side size of the carrom board is 3.872 units.

## 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.

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### What is the Square Root of 15 in Simplest Radical Form?

We must expush 15 as the product of its prime components i.e. 15 = 3 × 5. As such, as visible, the radical form of the square root of 15 cannot be simplified additionally. Therefore, the most basic radical create 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 = 3.872iwbelow i = √-1 and also it is called the imaginary unit.