Square root of 45 is 6.7082039325 it is a number which when multiplied by itself results in 45. Root of 45 is written as √45 or (45)^1/2. Simplified radical form of the square root of 45 is √(45) = 3√5.

In this article, we will learn about, What is Value of Root of 45, How to Find Square Root of 45, Examples related to the Value of Root 45, and others in detail.

What is Square Root of 45?

Square root of 45 is the number that is multiplied by itself to get 45. Value of square root of 20 is approximately equal to 6.708 and its value is calculated using various methods that are added below in the article,

• √45 = 6.708
• (45)^1/2 = 6.708

Square Root 45 Calculator

Square Root of 45 in Radical Form

Square root of 45 can be represented in radical form. Square root of 45 in radical form is expressed as follows:

√45 = √(3 × 3 × 5)

√45 = √(5) ×√(3)²

√(45) = 3√5

How to Find Square Root of 45?

You can use the following techniques that are given below to find the square root of 45;

• Square Root 45 Using Prime Factorization
• Square Root 45 Value by Long Division Method

Square Root 45 by Prime Factorization Method

Square root of 45 can be found easily using following steps added below,

Step 1: Break down 45 into prime factors. Hence, √45 =3 × 3 × 5 or 3² × 5.

Step 2: Take one factor from each pair and multiply them together: √45 ​= √(3 × 3) × 5.

Step 3: Combine Factors, 45 ​= (3² × 5​)

Step 4: Take square root, √45 ​= √(3² × 5​) = 3 × √5

So, square root of 45 is 3 √5 using Prime Factorization Methods.

Square Root 45 Value by Long Division Method

As, 45 is not a perfect square, we use long division method to find its square root. Long Division Method is the most suitable method to find the value of square root of non perfect square numbers. Follow the following steps to find the square root of 45 using the long division method:

Step 1: Write 45 as 45.000000. We will be using these zeroes for decimal division later on.

Step 2: Search for perfect square that is less than 45. In this case, it is 36.

Step 3: To obtain, 36 we will use 6 as divisor, hence, quotient at this point is 6 and remainder is 9.

Step 4: Put a decimal in the quotient and bring one pair of zeroes next to remainder 9 and add 6 in divisor

Step 5: Now we have 12 as new divisor and 900 as new dividend

Step 6: Now find a number for the unit place of divisor such that the same number can be placed in the quotient after the decimal and the resultant product of the divisor and the new number in quotient is smaller than or equal to the dividend. In this case, that number is 7 since 127 × 7 = 889 which is less than 900.

Step 7: Bring the next pair of zeroes down and repeat steps 4 and 5.

We calculate these values upto three decimal places to get an approximate value for square root of 45.

Is Square Root of 45 Rational or Irrational?

Root 45 is an Irrational Number. It is impossible to divide 45 into two such numbers such that there multiplication is exactly 45 so, square root of 45 approximately equal to 6.708, but in reality it is a non-terminating and non-recurring decimal number and thus, it is an irrational number.

√45 = 6.7082039325…

Solved Examples on Square Root of 45

Example 1: Evaluate √45 + 5.

Solution:

We know √45 = 6.7082 ≈ 6.71

Hence, √45 + 5 = 6.71 + 5 = 11.71.

Example 2: Simplify √45 × √5​.

Solution:

We have

√45 × √5 = √(45 × 5)

= √225 = 15

Example 3: If one side of a rectangle is √45​ units long and the other side is 2 units long, what is the area of the rectangle?

Solution:

We have,

Length of a rectangle = √45

Breadth of a rectangle = 2

Area of rectangle = length × breadth

Area of rectangle = √45 × 2

= 3√5 × 2 = 6√5 units.

Also, Check

• Square Root 1 to 30
• Square root of 1
• Square Root of 32
• Square Root of 24
• Square Root of 40

Square Root of 45 Value – FAQs

What is Root Value of 45?

Value of Square root of 45 is approximately equals to 6.7082 .

Is 45 a Prime Number?

No, 45 is not a prime number because it can b easily divisible by 3, 5, 9, and 15.

Is 45 a Perfect Square?

No, 45 is not a Perfect Square.

What is Square Root of 45 in Radical Form?

Square root of 45 in the radical form is √45.

What is Square of 45?

Square of 45 is 2025.

What is Square Root of 45 in Simplified Form?

Square root of 45 in simplified form is 3√5.