The square root of 15 is expressed as √15 in the radical kind and as (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 root of 15 in exponential form:**(15)½ or (15)0.5

**Square source 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 discover the Square root of 15? |

4. | FAQs ~ above Square root of 15 |

We know that enhancement has one inverse operation as subtraction and multiplication has actually 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 multiplied to itself to provide the number 15. So, we need to think the a number whose square is 15 through trial and error method, we deserve to see that, there does no exist any integer whose square is 15 yet we can discover the square root of 15 using the calculator and also we get, √15 approx 3.872983... Us can check this answer and also we surely room going to need a calculator here, 3.872983 × 3.872983...approx 14.999997318289... Phew! That"s fairly close come 15.

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

The square root of 15 is not a rational number. That is an irrational number. Here"s why. A rational number is a number that deserve to be expressed in the type of p/q, whereby p, q ∈ Z and q ≠ 0. A number is irrational if it is non-terminating with no repeating patterns in that is decimal part. Now let us look at the square root of 15, the decimal depiction of √15 is 3.87298334621... Perform you think the decimal component stops ~ 3.87298334621...? No, it is never-ending. It is a non-terminating decimal with non-repeating digits. The number 2.15215427125... can"t be created in p/q form, where p and q are integers. So, the square root of 15 is not a reasonable number. The is an irrational number.

## How to uncover the Square source of 15?

We will talk about two methods of finding the square source of 15. To express the radicand to it is in the product including perfect square(s) and simplifying itLong division method because that perfect and also non-perfect squares. Let"s comment on the first method, simplifying a square root way to rewrite the in such a method that there room no perfect squares left in the radicand. √50 can be streamlined to 5√2 but √15 cannot be streamlined further. Allow us learn the reason behind. **The element factorization the 15 is 15 = 3 × 5**. For simplifying √15 further we will need one or more pairs of 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 through long division is uncovered using the following steps:

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

**Step 2**: find a number that, when multiplied to itself, gives the product less than or same to 15 and also close to 15. So, the number is 3. Putting the divisor as 3, we gain the quotient as 3 (same together the divisor), we get the remainder to be 6

**Step 3:**Double the divisor and also enter it through a blank on the right. Assumption: v the largest feasible digit to to fill in the blank which will end up being the brand-new digit in the quotient, together that once the new divisor is multiply to the new quotient the resultant product is much less than or equal to the dividend. Divide and also write the remainder. Repeat this procedure to obtain the decimal places until friend want.

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

Similarly,

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

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

**Think Tank:**

Jenny has a square table that has an area the 15 square inches. She extended it with a table cloth of area 25 square inches. How plenty of inches does the fabric hang about the table on each side?

**Important Notes:**

The square source is the inverse procedure of squaring.The square source of 15 deserve to be expressed as √15 or 15½. It is one irrational number.We can discover 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)

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

**Solution**

We know that the area the 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 entirety number is 15. By recognize the square source of the area of 15 sq. Units, we can uncover the side length of the carrom board.Side that the square board = √15= 3.872.So, the side size of the carrom plank is 3.872 units.

## FAQs on the Square source of 15

### What is the value 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 element factorizing 15 i.e. 31 × 51, 3 is in strange power. Therefore, the square source of 15 is irrational.

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

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

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

We have to express 15 together the product of its prime determinants i.e. 15 = 3 × 5. Therefore, together visible, the radical form of the square root of 15 cannot be streamlined further. Therefore, the easiest radical type of the square root of 15 have the right to be created as √15

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

The square source of -15 is an imagine number. It can be written as √-15 = √-1 × √15 = ns √15 = 3.872iwhere ns = √-1 and it is dubbed the imagine unit.