Simplify Square Root Of 120

Square Root of 120

In this mini-lesson, we volition summate the square root of 120 by the long partition method along with solved examples and interactive questions. The square root of a number is the number that gets multiplied to itself to give the original number. four is a square root of xvi considering 4 × 4 = 16 and the symbol foursquare root is written as√and is an integral part of mathematics.
Let us take a await at what the square root of 120 is.

Square Root of 120: √120 = x.954
Square of 120: 120ⁱⁱ = 14400

ane.	What Is the Foursquare Root of 120?
two.	Is Square Root of 120 Rational or Irrational?
3.	How to Find the Square Root of 120?
4.	Important Notes on Square Root of 120
5.	FAQs on Square Root of 120
6.	Challenging Questions on Foursquare Root of 120

What Is the Square Root of 120?

The square root is an changed mathematical operation of a square. The square root of a number is the number that gets multiplied to itself to give the product. The square root of 120 is represented as√120. The square root of 120 in the exponent form is expressed equally 120^1/2. The square root of 120 rounded to iii decimal places is 10.954

Is the Square Root of 120 Rational or Irrational?

A rational number is a number that is of the class p/q where:

p and q are integers
q is not equal to 0

A number that cannot be expressed as a ratio of two integers is an irrational number. Non-terminating decimals having repeated numbers after the decimal point are rational numbers. Now let united states of america look at the foursquare root of 120.The decimal representation is:√120 = 10.9544511501. Exercise you call up the decimal part stops after 10.9544511501? No, it is never-ending therefore it is a non-terminating decimal with non-repeating numbers. The number ten.9544511501.. can't be written in p/q class. So √120 is an irrational number.

How to Find the Foursquare Root of 120?

Square Root of 120 can exist calculated using diverse methods:

By simplifying the radical of the numbers that are perfect squares.
By long division method for perfect and non-perfect squares

Simplified Radical Form of Square Root of 120

To simplify the square root of 120, let us first limited 120 every bit a product of its prime factors. Thus the prime factorization of 120 is: 2 × 2 × ii × iii × 5. To detect the foursquare root of whatever number, we accept i number from each pair of the same numbers from its prime factorization and we multiply them.
120 = 2 × ii × ii × three × 5
√120 =√(2 × 2 × 2 × iii × 5)
= 2 ×√(2 × 3 × five)
= 2√30
Thus nosotros have expressed the square root of 120 in the simplest radical form every bit 2√thirty
Then,√120 = 2√30. The value of the square root of eleven past long sectionalization method consists of the following steps:

Step 1: Starting from the right, nosotros will pair up the digits by putting a bar in a higher place them.
Step 2: At present, we find a number such that the square of any number gives a product less than or equal to the first pair. Here, the first pair merely consists of 1 number, i.e. 1. Square of 1 gives product i. The number is subtracted from the first pair and subsequently, the next pair is added equally the divisor, i.e. 20
Footstep 3: Now we accept the double of quotient and place a digit with divisor along with its placement in the quotient, such that the new divisor, when multiplied with the individual number in the caliber, gives the product less than the dividend, subsequently subtracting information technology from the dividend.
Stride 4: For the new dividend obtained, nosotros take the double of quotient and place a digit with divisor forth with its placement in the quotient, such that the new divisor when multiplied with the individual number in caliber gives the product less than the dividend.
Step 5: The difference is obtained in the to a higher place step. The double of the quotient is again taken and used as a divisor along with the involvement of i more than digit such that the same digit is mentioned in the quotient resulting in a product less than the new divisor.
Pace half dozen: The process is repeated the same fashion.

Therefore, the segmentation is shown as:

square root of 120

Explore Square roots using illustrations and interactive examples

Square Root of 25
Square Root of 100
Square Root of 121
Square Root of 225
Square Root of 45

Important Notes:

The prime factorization method is used to write a square root of a non-perfect foursquare number in the simplest radical form.
For example: 45 = 3 × 3 × v = iii² × 35
Irrational numbers cannot be expressed as a ratio of two integers. Instance: pi,√2
The square root of 120 in the radical form is expressed every bit 2√thirty

Challenging Questions:

Can you call back of whatsoever quadratic equation which has a root as√120?
Is √-120 a real number?

Example 1: John is asked to find the square root of 100 using the laws of exponents. Can yous assistance him?

Solution

The square root can exist always replaced with the exponent ane/2.
√100 = 100^ane/two
= (102)ane/ii [ 102 = 100]
= 10
Thus,√100 = 10
Example 2: Jack buys a new square carpet for his living room. He finds a square carpeting that has an expanse of 36 sq feet. What should be the length of the sides of his square carpet?

Solution

The area of the square rug is 36 square anxiety.
The length of each side of the carpet is the square root of its area.
The square root of 36 is 6.
Therefore, the length of each side of the carpet is half dozen feet.

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FAQs On Square Root of 120

What is the square root of 120?

The square root of 120 is 4.6904

Why is √120 an irrational number?

A number with decimal expansion as non-terminating and non-repeating is always an irrational number. So, √120 is an irrational number.

Is the square root of 120 infinite?

The decimal expansion of √120 is infinite considering information technology is non-terminating and non-repeating.

Is the foursquare root of 120 an irrational number?

Yep, the square root of 120 is an irrational number.

Is square root of 120 a real number?

Yes, the square root of 120 is a real number.