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Square Root of 16
The square root of 16 is expressed as √16 in the radical form and as (16)½ or (16)0.5 in the exponent form. The square root of 16 is 4. It is the positive solution of the equation x2 = 16. The number 16 is a perfect square.
- Square Root of 16: 4
- Square Root of 16 in exponential form: (16)½ or (16)0.5
- Square Root of 16 in radical form: √16
|1.||What Is the Square Root of 16?|
|2.||Is Square Root of 16 Rational or Irrational?|
|3.||How to Find the Square Root of 16?|
|4.||FAQs on Square Root of 16|
What Is the Square Root of 16?
The square root of a number is the number that gets multiplied to itself to give the product. For any two real numbers a and b,
a2 = b
a = √b
The above expression means that a is the 2nd root or square root of b. The square root of 16 means that number which when multiplied with itself will give the result as 16. The definition above can be represented as,
Square root of 16 = √16
42 = 4 × 4 is 16
Here 4 is called the square root of 16
16 is a perfect square.
So the square root of 16 is 4. The square root of 16 is the inverse operation of squaring 4 and -4
4 × 4 = 16
(-4) × (-4) = 16
Is the Square Root of 16 Rational or Irrational?
A rational number is defined as the number that can be expressed in the form of a quotient or division of two integers i.e., p/q, where q = 0. In the above section, we observed diagrammatically that the square root of 16 is either 4 or (-4) Both the numbers can be represented in the form of a rational number i.e., 4/1 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 square root of 16 can be calculated using different methods: Prime Factorization and Long Division method. Let us see how it is calculated using Prime Factorization:
Square Root of 16 by Prime Factorization
Following steps can be followed using prime factorization:
- Step 1. Determine the prime factorization of 16
16 = 2 × 2 × 2 × 2
16 = 2 × 2
- Step 2. Group the prime factors obtained for 16 in pairs.
- Step 3. Pick one factor from each pair and they can be written in the form:
- Step 4. Thus, following the law of exponents, we get,
√16 = √ (2 × 2)2
√16 = (42)½ = 4
Let us now try finding the square root of 16 by the long division method!
Square Root of 16 By Long Division
Here are the steps that need to be followed to calculate the square root of 16:
- Step 1. Write 16 as shown in the figure. Start grouping the number in pairs from the right end. For 16, both the numbers will be grouped under one bar.
- Step 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 4 as the divisor.
- Step 4. The quotient obtained from the long division is the square root of 16
Explore Square roots using illustrations and interactive examples
- Jenny has a square table that has an area of 16 square inches. She covered it with a table cloth of area 25 square inches. How many inches does the cloth hang over the table on each side if put centered?
- The square root of 16 is expressed as √16 in the radical form and as 161/2 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 will be 4.
Square Root of 16 Solved Examples
Example 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 be on each side?
Total cubes used by Noah to make a square surface arrangement = 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) = 4
Since the number of cubes used cannot be negative, practically, we will only take the positive value.
Hence, bricks on each side of the square = 4
Example 2: Jake had arranged 16 flower plants in a square bed. He got some extra flower plants and tried to keep the flower bed arrangement square after adding them. If the total number of flower plants in the new bed is 36, how many extra plants are added in each row?
We know, each side of the square = √Area
We will use the same concept to find the flowers in each row.
Initially with 16 flower plants, flower plants in each row = √16 = 4 flowers
We neglect the negative value of the square root when it is practically not applicable. Therefore, we did not use - 4 value in this example.
For the arrangement with 36 flowers, flower 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 16√3 in2. Find the length of one of the sides of the triangle.
Let 'a' be the length of one of the sides of the equilateral triangle.
⇒ Area of the equilateral triangle = (√3/4)a2 = 16√3 in2
⇒ a = ±√64 in
Since length can't be negative,
⇒ a = √64 = 2 √16
We know that the square root of 16 is 4.
⇒ a = 8 in
FAQs on the Square Root of 16
What is the Value of the Square Root of 16?
The square root of 16 is 4.
Why is the Square Root of 16 a Rational Number?
Upon prime factorizing 16 i.e. 24, we find that all the prime factors are in even power. This implies that the square root of 16 is a positive integer. Therefore, the square 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 √16 = 19 + 17 × 4 = 19 + 68 = 87
Is the number 16 a Perfect Square?
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 16 is 4. Find the Value of the Square Root of 0.16.
Let us represent √0.16 in p/q form i.e. √(16/100) = 4/10 = 0.4. Hence, the value of √0.16 = 0.4