Evaluate Square Root Of 16

Square Root of 16

The square root of 16 is expressed every bit √16 in the radical grade and as (16)^½ or (16)^0.v in the exponent form. The foursquare root of 16 is iv. It is the positive solution of the equation xⁱⁱ = 16. The number 16 is a perfect square.

Square Root of 16: 4
Square Root of 16 in exponential form: (16)^½ or (xvi)^0.5
Square Root of 16 in radical form: √16

ane.	What Is the Square Root of xvi?
2.	Is Square Root of 16 Rational or Irrational?
iii.	How to Find the Foursquare Root of 16?
4.	FAQs on Square Root of 16

What Is the Square Root of sixteen?

The foursquare root of a number is the number that gets multiplied to itself to give the product. For any two existent numbers a and b,

a²= b

a =√b

The above expression means that a is the 2nd root or square root of b. The foursquare root of 16 means that number which when multiplied with itself will give the result equally 16. The definition higher up can be represented as,

Foursquare root of sixteen =√sixteen

4ⁱⁱ= 4 × 4 is 16
Here 4 is called the square root of 16
16 is a perfect square.
And then the foursquare root of xvi is four. The square root of 16 is the inverse operation of squaring iv and -4
iv × four = sixteen
(-4) × (-4) = 16

Is the Foursquare Root of 16 Rational or Irrational?

A rational number is defined as the number that can be expressed in the grade of a quotient or partitioning of two integers i.eastward., p/q, where q = 0. In the above section, we observed diagrammatically that the square root of sixteen is either iv or (-iv) Both the numbers can exist represented in the course of a rational number i.due east., 4/1 and -(4/one) respectively.
√16 = iv = iv/one
Thus, the square root of 16 is rational.
So√16 is an irrational number.

How to Detect the Square Root of 16?

The foursquare root of 16 can be calculated using dissimilar methods: Prime Factorization and Long Division method. Permit the states see how it is calculated using Prime Factorization:

Square Root of xvi by Prime Factorization

Post-obit steps can exist followed using prime factorization:

Step ane.Determine the prime number factorization of sixteen
16 = 2 × 2 × 2 × 2
xvi = 2 × 2
Step 2.Group the prime factors obtained for 16 in pairs.
Step 3.Choice 1 factor from each pair and they can be written in the grade:
Step four. Thus, following the law of exponents, we become,

√16 = √ (2 × 2)ⁱⁱ

√xvi = (4²)^½ = four

Permit us now try finding the foursquare root of 16 by the long segmentation method!

Square Root of 16 By Long Partition

Here are the steps that demand to be followed to calculate the foursquare root of sixteen:

Step i. Write 16 as shown in the effigy. Start group the number in pairs from the right end. For 16, both the numbers will exist grouped under ane bar.
Footstep 2. Find the largest number that when multiplied with itself will give 16 or a smaller number closest to 16. 4 is the required number.
Step 3. Perform division on the dividend 16, using four as the divisor.
Pace four.The quotient obtained from the long division is the square root of xvi

square root of 16 by long division

Explore Square roots using illustrations and interactive examples

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Remember Tank:

Jenny has a foursquare tabular array that has an area of sixteen square inches. She covered information technology with a tabular array cloth of area 25 square inches. How many inches does the fabric hang over the table on each side if put centered?

Of import Notes:

The foursquare root of 16 is expressed as√xvi in the radical course and as xvi^i/two in exponential form.
The square root of a number is both negative and positive for the aforementioned numerical value i.e., the square root of 16 will be four.

Square Root of sixteen Solved Examples

Example 1: Noah has a bag filled with cubes. 9 of them are green and 7 are orange. If she makes a foursquare arranging them together, how many bricks will exist on each side?

Solution

Total cubes used past Noah to make a square surface system = 9 + 7 = 16 cubes
Number of cubes on each side of square = √Total cubes required to make the square
Cubical bricks on each side of the cube = √16 = √ (4 × 4) = four
Since the number of cubes used cannot be negative, practically, nosotros will only take the positive value.
Hence, bricks on each side of the square = 4
Instance 2: Jake had arranged xvi bloom plants in a square bed. He got some extra flower plants and tried to continue the flower bed organization square after adding them. If the full number of flower plants in the new bed is 36, how many actress plants are added in each row?

Solution

We know, each side of the square = √Area
Nosotros volition use the same concept to find the flowers in each row.
Initially with xvi flower plants, flower plants in each row = √16 = 4 flowers
We fail the negative value of the square root when it is practically not applicative. Therefore, we did non use - 4 value in this example.
For the system with 36 flowers, flower plants in each row = √36 = 6 flowers
Thus, extra flowers added in each row = half dozen - 4 = 2 flowers
Example 3: If the expanse of an equilateral triangle is 16√3 in². Find the length of one of the sides of the triangle.

Solution:

Permit 'a' be the length of ane of the sides of the equilateral triangle.
⇒ Area of the equilateral triangle = (√3/4)a² = sixteen√3 in^two
⇒ a = ±√64 in
Since length can't be negative,
⇒ a = √64 = ii √xvi
We know that the foursquare root of xvi is 4.
⇒ a = 8 in

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FAQs on the Foursquare Root of xvi

What is the Value of the Foursquare Root of sixteen?

The square root of xvi is four.

Why is the Square Root of 16 a Rational Number?

Upon prime number factorizing 16 i.eastward. two⁴, we find that all the prime factors are in even power. This implies that the square root of xvi is a positive integer. Therefore, the foursquare root of 16 is rational.

Evaluate 19 plus 17 square root 16

The given expression is 19 + 17 √16. We know that the square root of 16 is 4. Therefore, 19 + 17 √xvi = 19 + 17 × 4 = xix + 68 = 87

Is the number 16 a Perfect Square?

The prime number factorization of sixteen = ii⁴. Here, all the numbers are in the ability of 2. This implies that the square root of 16 is a positive integer. Therefore, 16 is a perfect foursquare.

What is the Value of 17 square root 16?

The square root of 16 is 4. Therefore, 17 √16 = 17 × 4 = 68.

If the Square Root of sixteen is 4. Discover the Value of the Square Root of 0.xvi.

Permit us correspond √0.16 in p/q form i.due east. √(16/100) = 4/10 = 0.iv. Hence, the value of √0.sixteen = 0.4