Negative Square Root Of 16

Square Root of sixteen

The square root of 16 is expressed as √16 in the radical class and as (sixteen)^½ or (16)^0.5 in the exponent class. The square root of xvi is 4. It is the positive solution of the equation x² = 16. The number xvi is a perfect foursquare.

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

1.	What Is the Square Root of sixteen?
two.	Is Foursquare Root of sixteen Rational or Irrational?
three.	How to Find the Square Root of 16?
4.	FAQs on Square Root of 16

What Is the Foursquare Root of 16?

The foursquare root of a number is the number that gets multiplied to itself to requite 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 requite the outcome as 16. The definition higher up can exist represented as,

Square root of xvi =√16

iv²= 4 × 4 is sixteen
Here four is called the square root of 16
16 is a perfect square.
So the foursquare root of 16 is four. The foursquare root of 16 is the changed operation of squaring four and -4
4 × 4 = 16
(-4) × (-4) = 16

Is the Foursquare Root of sixteen Rational or Irrational?

A rational number is divers as the number that can be expressed in the course of a caliber or division of two integers i.due east., p/q, where q = 0. In the to a higher place department, nosotros observed diagrammatically that the square root of xvi is either 4 or (-4) Both the numbers can be represented in the class of a rational number i.e., 4/one and -(4/1) respectively.
√16 = 4 = 4/1
Thus, the square root of 16 is rational.
So√16 is an irrational number.

How to Find the Square Root of 16?

The foursquare root of xvi can be calculated using dissimilar methods: Prime Factorization and Long Sectionalization method. Let us see how it is calculated using Prime Factorization:

Square Root of xvi past Prime Factorization

Following steps can be followed using prime factorization:

Step 1.Determine the prime number factorization of 16
16 = 2 × 2 × 2 × 2
16 = 2 × 2
Pace ii.Group the prime factors obtained for sixteen in pairs.
Footstep 3.Pick i factor from each pair and they can be written in the form:
Step four. Thus, following the law of exponents, we get,

√xvi = √ (2 × two)²

√16 = (4ⁱⁱ)^½ = 4

Let united states of america now try finding the square root of sixteen by the long division method!

Square Root of 16 Past Long Division

Here are the steps that need to be followed to calculate the foursquare root of xvi:

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

square root of 16 by long division

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Call up Tank:

Jenny has a square table that has an area of 16 square inches. She covered it with a table material of expanse 25 square inches. How many inches does the textile hang over the table on each side if put centered?

Important Notes:

The square root of 16 is expressed every bit√sixteen in the radical grade and as 16^i/2 in exponential form.
The square root of a number is both negative and positive for the same numerical value i.e., the square root of 16 volition be 4.

Foursquare Root of 16 Solved Examples

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

Solution

Total cubes used past Noah to make a foursquare surface arrangement = 9 + 7 = xvi cubes
Number of cubes on each side of square = √Total cubes required to brand the square
Cubical bricks on each side of the cube = √16 = √ (4 × iv) = 4
Since the number of cubes used cannot be negative, practically, we will but take the positive value.
Hence, bricks on each side of the foursquare = 4
Example two: Jake had bundled 16 blossom plants in a square bed. He got some extra bloom plants and tried to go along the flower bed arrangement square later on adding them. If the total number of bloom plants in the new bed is 36, how many extra plants are added in each row?

Solution

We know, each side of the square = √Area
We will use the same concept to find the flowers in each row.
Initially with 16 blossom plants, flower plants in each row = √xvi = 4 flowers
We neglect the negative value of the square root when it is practically not applicable. Therefore, we did not utilise - iv value in this example.
For the arrangement with 36 flowers, bloom plants in each row = √36 = 6 flowers
Thus, extra flowers added in each row = 6 - 4 = 2 flowers
Example 3: If the area of an equilateral triangle is sixteen√iii inⁱⁱ. Find the length of one of the sides of the triangle.

Solution:

Permit 'a' be the length of one of the sides of the equilateral triangle.
⇒ Surface area of the equilateral triangle = (√3/4)a² = xvi√iii inⁱⁱ
⇒ a = ±√64 in
Since length tin can't exist negative,
⇒ a = √64 = 2 √16
Nosotros know that the square root of 16 is iv.
⇒ a = eight in

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FAQs on the Square Root of 16

What is the Value of the Square Root of 16?

The square root of xvi is iv.

Why is the Square Root of 16 a Rational Number?

Upon prime factorizing xvi i.e. 2^four, we observe that all the prime factors are in even ability. This implies that the square root of xvi is a positive integer. Therefore, the square root of 16 is rational.

Evaluate nineteen plus 17 square root 16

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

Is the number xvi a Perfect Square?

The prime factorization of sixteen = 2⁴. Hither, all the numbers are in the power of 2. This implies that the foursquare root of 16 is a positive integer. Therefore, 16 is a perfect square.

What is the Value of 17 foursquare root 16?

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

If the Square Root of 16 is 4. Find the Value of the Square Root of 0.16.

Let us correspond √0.16 in p/q form i.e. √(sixteen/100) = four/10 = 0.4. Hence, the value of √0.16 = 0.4