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

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**Square source 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 source of 15 Rational or Irrational? |

3. | How to find the Square root of 15? |

4. | FAQs top top Square source of 15 |

We understand that addition has one inverse procedure as subtraction and also multiplication has an inverse operation as division. Similarly, finding the square root is an inverse procedure of squaring. The square root of 15 is the number that gets multiply to chin to give the number 15. So, we need to think of a number who square is 15 through trial and also error method, we have the right to see that, there does no exist any integer who square is 15 yet we can uncover the square source of 15 using the calculator and we get, √15 approx 3.872983... We can check this answer and also we surely space going to need a calculator here, 3.872983 × 3.872983...approx 14.999997318289... Phew! That"s rather close to 15.

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

The square source of 15 is no a rational number. That is an irrational number. Here"s why. A rational number is a number that can be express in the type of p/q, wherein p, q ∈ Z and q ≠ 0. A number is irrational if it is non-terminating through no repeating patterns in that 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 through non-repeating digits. The number 2.15215427125... can"t be composed 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 discover the Square source of 15?

We will discuss two approaches of finding the square source of 15. Express the radicand to be the product entailing perfect square(s) and simplifying itLong division method for perfect and non-perfect squares. Let"s talk about the first method, simple a square root means to rewrite the in such a means that there room no perfect squares left in the radicand. √50 can be simplified to 5√2 but √15 cannot be streamlined further. Allow us discover the reason behind. **The element factorization of 15 is 15 = 3 × 5**. Because that simplifying √15 further we will require one or more pairs the the exact same factors. Such pairs of factors are no available. Therefore, √15 cannot be streamlined further.

### Square root of 15 By Long Division

The worth of the square root of 15 by long department is discovered using the adhering to steps:

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

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

**Step 3:**Double the divisor and also enter it with a blank on the right. Guess the largest feasible digit to fill in the empty which will become the brand-new digit in the quotient, together that once the new divisor is multiplied to the new quotient the result product is much less than or equal to the dividend. Divide and also write the remainder. Repeat this procedure to get the decimal places until girlfriend want.

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

Similarly,

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

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

**Think Tank:**

Jenny has actually a square table that has actually an area the 15 square inches. She covered it v a table cloth of area 25 square inches. How countless inches walk the fabric hang roughly the table on every side?

**Important Notes:**

The square source is the inverse procedure of squaring.The square source of 15 have the right to be expressed as √15 or 15½. That is one irrational number.We can uncover the square source of 15 using the long division method. The square source of 15 by long division method = 3.872 (to 3 decimal places)

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

**Solution**

We recognize 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 root of the area of 15 sq. Units, we can uncover 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 source of 15

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

The square source of 15 is 3.87298.

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

Upon element 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 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 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 source of 15 in most basic Radical Form?

We have to express 15 as the product of its prime components i.e. 15 = 3 × 5. Therefore, together visible, the radical type of the square root of 15 cannot be streamlined further. Therefore, the most basic radical type of the square source of 15 can be created as √15

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

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