The square source of 15 is expressed as √15 in the radical kind and together (15)½ or (15)0.5 in the exponent form. The square source of 15 rounded approximately 8 decimal locations is 3.87298335. The is the positive solution that the equation x2 = 15.

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**Square root of 15:**3.872983346207417

**Square source of 15 in exponential form:**(15)½ or (15)0.5

**Square root of 15 in radical form:**√15

1. | What Is the Square source of 15? |

2. | Is Square root of 15 Rational or Irrational? |

3. | How to uncover the Square source of 15? |

4. | FAQs top top Square root of 15 |

We know that addition has one inverse operation as subtraction and multiplication has an inverse operation as division. Similarly, recognize the square root is one inverse operation of squaring. The square source of 15 is the number that gets multiply to itself to offer the number 15. So, we have to think that a number whose square is 15 through trial and error method, we can see that, there does no exist any type of integer whose square is 15 but we can uncover the square source of 15 using the calculator and also we get, √15 approx 3.872983... We can examine this answer and we surely are going to require a calculator here, 3.872983 × 3.872983...approx 14.999997318289... Phew! That"s quite close to 15.

## Is the Square source of 15 Rational or Irrational?

The square source of 15 is not a rational number. That is an irrational number. Here"s why. A reasonable number is a number that have the right to be express in the form of p/q, whereby p, q ∈ Z and q ≠ 0. A number is irrational if that is non-terminating with no repeating patterns in the decimal part. Now let united state look in ~ the square source of 15, the decimal depiction of √15 is 3.87298334621... Execute you think the decimal part stops after 3.87298334621...? No, that is never-ending. That is a non-terminating decimal with non-repeating digits. The number 2.15215427125... can"t be composed in p/q form, whereby p and q are integers. So, the square source of 15 is not a reasonable number. The is an irrational number.

## How to discover the Square source of 15?

We will comment on two approaches of detect the square source of 15. Refer the radicand to be the product including perfect square(s) and also simplifying itLong division method for perfect and non-perfect squares. Let"s comment on the an initial 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. Allow us learn the factor behind. **The element factorization that 15 is 15 = 3 × 5**. Because that simplifying √15 further us will need one or more pairs the the exact same factors. Together pairs of determinants are no available. Therefore, √15 cannot be simplified further.

### Square source of 15 By Long Division

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

**Step 1**: beginning from the right, we will certainly pair up the digits by putting a bar above them.

**Step 2**: discover a number that, as soon as multiplied to itself, gives the product less than or same to 15 and close come 15. So, the number is 3. Placing the divisor as 3, we gain the quotient as 3 (same together the divisor), we acquire the remainder to be 6

**Step 3:**Double the divisor and also enter it with a empty on its right. Guess: v the largest possible digit to fill in the blank which will end up being the brand-new digit in the quotient, together that as soon as the brand-new divisor is multiplied to the brand-new quotient the resultant product is much less than or equal to the dividend. Divide and write the remainder. Repeat this process to get the decimal areas until friend want.

The square root of 15 by long division method = 3.872 (to 3 decimal places)

Similarly,

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

**Explore Square roots making use of illustrations and also interactive examples**

**Think Tank:**

Jenny has actually a square table that has actually an area of 15 square inches. She spanned it with a table cloth of area 25 square inches. How numerous inches go the cloth hang about the table on every side?

**Important Notes:**

The square root is the inverse procedure of squaring.The square source of 15 can be expressed as √15 or 15½. The is an irrational number.We can uncover the square source of 15 using the long department method. The square root of 15 by long department method = 3.872 (to three decimal places)

**Example 2**: Mathew has actually a carrom board of area 15 sq. Units. That measured the size of the carrom plank to be 3.872 units. Why is that so?

**Solution**

We understand that the area that 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 the nearest entirety number is 15. By detect the square source of the area that 15 sq. Units, we can find the side size of the carrom board.Side of the square plank = √15= 3.872.So, the side size of the carrom board is 3.872 units.

## FAQs ~ above the Square root of 15

### What is the worth of the Square root of 15?

The square root of 15 is 3.87298.

### Why is the Square source of 15 one Irrational Number?

Upon prime factorizing 15 i.e. 31 × 51, 3 is in odd power. Therefore, the square source of 15 is irrational.

### What is the value of 5 square source 15?

The square root of 15 is 3.873. Therefore, 5 √15 = 5 × 3.873 = 19.365.

### What is the Square that the Square source of 15?

The square of the square source of 15 is the number 15 chin i.e. (√15)2 = (15)2/2 = 15.

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### What is the Square root of 15 in easiest Radical Form?

We should express 15 together the product the its prime components i.e. 15 = 3 × 5. Therefore, as visible, the radical form of the square root of 15 can not be simplified further. Therefore, the easiest radical type of the square source of 15 deserve to be written as √15

### What is the Square source of -15?

The square root of -15 is an imaginary number. It deserve to be created as √-15 = √-1 × √15 = ns √15 = 3.872iwhere i = √-1 and also it is referred to as the imagine unit.