The square root of 5 is expressed as √5 in the radical form and as (5)^{½} or (5)^{0.5} in the exponent form. The square root of 5 rounded up to 5 decimal places is 2.23607. It is the positive solution of the equation x^{2} = 5.

**Square Root of 5:**2.23606797749979**Square Root of 5 in exponential form:**(5)^{½}or (5)^{0.5}**Square Root of 5 in radical form:**√5

1. | What Is the Square Root of 5? |

2. | IsSquare Root of 5Rational or Irrational? |

3. | How to Find the Square Root of 5? |

4. | Challenging Questions |

5. | Important Notes on Square Root of 5 |

6. | FAQs on Square Root of 5 |

## What Is the Square Root of 5?

Let us first understand the meaning of square root. Thesquare root of a number is the number which,when multiplied to itself,gives the product as the original number. Consider the example:

- 5
^{2}= 5× 5is 25

Here 5 is called the square root of 25. 25is a perfect square. So** the square root of 25 is 5.**Now, what is thesquare root of 5? Does that mean non-square numbers cannot have a square root? Non-square numbers also have a square root, just that they are notwhole numbers. For real numbers aand b,

- a
^{2}=b isa=√b

The square root of 5in the radical form is expressed as√5and inexponentform, it is expressed as 5½. The square root of 25is the inverse operation of squaring 5and -5

- 5 × 5=25
- (-5)× (-5) = 25.

Let us look at the square root of 5

### Square Root of 5

We know that factors of 5 are 5× 1 = 5

- √5= 2.23
- 5 is not a perfect square.

## Is the Square Root of 5Rational orIrrational?

A number that can be expressed as a ratio of twointegers, that is, p/q, q ≠ 0is called arational number. Now let us look at the square root of 25. √25= 5 = 5/1. Thus, √25is a rational number. Now let us look at the square root of 5

- √5 = 2.23

A number that cannot be expressed as a ratio of two integersis called an irrational number.

- 5is not a perfect square.
- The square root of 5 is an irrational number.

## How to Find the Square Root of 5?

There are different methodsto findthe square root of 5. The first method is by prime factorization and the second is the conventional long divisionmethod.

### Square Root of 5 Using Prime Factorization

Let us find the square root of 5using prime factorization:

- 5 = 5× 1
- 5 = 5

Taking square root

- √5 =√5
- √5= 2.23

Let us now try finding the square root of 5by the long division method.

### Square Root of 5ByLong Division

Let us follow these steps to find the square root of 5by the long division method.

- Step 1:Group the digits into pairs (for digits to the left of the decimal point, pair them from right to left) by placing a bar over them. Since our number is 5, let us represent itinside the division symbol.
- Step 2:Find the largest number such that when you multiply it with itself, the product is less than or equal to 5. We know that2×2is 4and is less than 5. Now let us divide 5by 2
- Step 3: Let us place a decimal point and pairs of zeros and continue our division. Now, multiply the quotient by 2 and the product becomes the starting digit of our next divisor.
- Step 4: Choose anumber in the unit's place for the new divisor such thatits product with a number is less than or equal to 100. We know that 2is in the ten's place and our product has to be 100and the closest multiplication is42× 2= 84
- Step 5:Bring down the next pair of zerosand multiply the quotient 22(ignore the decimal) by 2, which is 44and the starting digit of the new divisor.
- Step 6: Choose the largestdigit in the unit's place for the new divisor such that theproduct of the new divisor with thedigit at one's placeis less than or equal to 1600. We see that 443, when multiplied by 3, gives1329which is less than 1600. Our long division now looks like

- Step 7: Add morepairs of zeros and repeat the process offinding the new divisor and product as in step 2

Note that the square root of 5is an irrational number,i.e, it is never-ending.So,stopthe process after 4 or5 iterations,and you have the square root of 5by the long division method.

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

- Square Root of 25
- Square Root of 35
- Square Root of 65
- Square Root of 85
- Square Root of 15

**Challenging Questions:**

Evaluate the following:

a) 5√25 + 5√4 + 5√16

b) 5√5+ 7√5 - 10√5

c) 5√6 + 5√25 - 5

**Important Notes:**

- The square root of 5in the radical form is expressed as √5.
- In exponent form, the square root of 5is expressed as 5
^{½}.