Square Root of 17
The square root of 17 is expressed as √17 in the radical form and as (17)½ or (17)0.5 in the exponent form. The square root of 17 rounded up to 7 decimal places is 4.1231056. It is the positive solution of the equation x2 = 17.
- Square Root of 17: 4.123105625617661
- Square Root of 17 in exponential form: (17)½ or (17)0.5
- Square Root of 17 in radical form: √17
|1.||What Is the Square Root of 17?|
|2.||Is Square Root of 17 Rational or Irrational?|
|3.||How to Find the Square Root of 17?|
|4.||FAQs on Square Root of 17|
What Is the Square Root of 17?
- The square root of a number is the number that gets multiplied to itself to give the original number.
- √17 = 4.123 × 4.123
Is the Square Root of 17 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.
- The square root of 17 is either 4.12310562562 or (-4.12310562562)
- Both the numbers cannot be represented in the form of a rational number and have a non terminating non-repeating decimal trail.
- Thus, the square root of 17 is irrational.
How to Find the Square Root of 17?
The square root of a number can be calculated using different methods:
- Prime Factorization
- Long Division method
- and by approximation
√17 cannot be simplified any further.
Square Root of 17 by Long Division Method
- Step 1 : Write 17 as shown in the figure. Start grouping the number in pairs from the right end. For 17, both the numbers will be grouped under one bar.
- Step 2: Find the largest number, which, when multiplied with itself, will give 17 or a smaller number closest to 17. 4 is the required number.
- Step 3 : Divide 17 by 4
- Step 4: We get the remainder as 1 in this step. Now, place 3 pairs of zeros after the decimal point and continue the long division. Bring one pair of zeros down. Add the quotient 4 to the divisor, which is also 4. Thus, 8 will be placed as the new divisor on the tens place, with a blank on one's place. This blank will be filled by a number which when multiplied with the quotient, will give the result 100 or a smaller number closest to 100. Here, ( 81 × 1 = 81) is the closest to 100. So 1 will be placed on the blank place.
- Step 5: The remainder of this step is 19. Now, bring down the second pair of zeros. Repeating the above step, the quotient from the previous step, which is 1, will be added to the divisor from the previous step (81). 82 along with a blank on digit in ones will be the new divisor. Note that we will not use the complete quotient, but only the previous step quotient.
- Step 6: We will repeat the process of Step 4. As 822 × 2 = 1644 is the closest to 1900. Again follow the same procedure for the remainder 256 by bringing down another pair of zeros down. So, the approximate value of √17 = 4.123
Explore Square roots using illustrations and interactive examples
- Jenny has a square table that has an area of 17 square inches. She covered it with a table cloth of area 25 square inches. How many inches does the cloth hang around the table on each side?
- The square root of 17 is expressed as √17 in the radical form and as 171/2 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 17 will be both + 4.12310562562 or - 4.12310562562
- 17 lies between 16 and 25. So√17 lies between √16 and √25
- The prime factorization method is used to write a square root of a non-perfect square number in the simplest radical form.
Square Root of 17 Solved Examples
Example 1: Noah orders a pie whose surface area is 53.397 square inches. What is the radius of the pie that he ordered?
The total surface area of Noah's pie = 53.397 square inches
Surface area of a circle = pi r2
Therefore, 53.397 = 3.141 × r2
r2 = 53.397 ÷ 3.141
r = + 4.123 or -4.123
Since the radius cannot be negative, we will take the positive value.
Hence, the radius of the pie that Noah ordered = 4.123 inches.
Example 2 : Kim is covering her square-shaped bathroom floor with tiles. If there are a total of 20 squared tiles and the area of the bathroom floor is 340 square inches, find the length of each side of a single tile. ?
We know, each side of square = Area
We will use the same concept to find the dimension of each tile.
Area of bathroom = the area of 20 tiles, which is given as 340 square inches.
Area of each tile = 340 ÷ 20 = 17 square inches
Length of each side of tile = √17 = 4.1231 inches
Example: If the surface area of a sphere is 68π in2. Find the radius of the sphere.
Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr2 = 68π in2
⇒ r = ±√17 in
Since radius can't be negative,
⇒ r = √17
The square root of 17 is 4.123.
⇒ r = 4.123 in
FAQs on the Square Root of 17
What is the Value of the Square Root of 17?
The square root of 17 is 4.1231.
Why is the Square Root of 17 an Irrational Number?
The number 17 is prime. This implies that the number 17 is pairless and is not in the power of 2. Therefore, the square root of 17 is irrational.
Evaluate 17 plus 15 square root 17
The given expression is 17 + 15 √17. We know that the square root of 17 is 4.123. Therefore, 17 + 15 √17 = 17 + 15 × 4.123 = 17 + 61.847 = 78.847
What is the Square Root of 17 in Simplest Radical Form?
The number 17 is a prime number. This implies that the number 17 is pairless and is not in the power of 2. Therefore, the radical form of square root of 17 cannot be simplified further.
What is the Value of 1 square root 17?
The square root of 17 is 4.123. Therefore, 1 √17 = 1 × 4.123 = 4.123.
Is the number 17 a Perfect Square?
The number 17 is prime. This implies that the square root of 17 cannot be expressed as a product of two equal integers. Therefore, the number 17 is not a perfect square.