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.

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What Is the Square Root of 17?


√17 = 4.123 ×4.123

Is the Square Root of 17 Rational orIrrational?

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 numbercan be calculatedusing different methods:

Prime FactorizationLong Division methodand 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 smallernumber closest to 17. 4 is the required number.Step 3 :Divide 17 by 4Step 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, 8will 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 multipliedwith 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 ondigit in oneswill 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. As822 ×2 = 1644is 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

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Explore Square roots using illustrations and interactive examples


Challenging Questions:


Jenny has a square table that has an area of 17square inches. She covered it with a table cloth of area 25square inches.How many inchesdoes the cloth hang around the table on each side?

Important Notes:


The square root of 17 is expressed as √17 in the radical form and as 171/2in 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- 4.1231056256217 lies between 16and 25. So√17lies between √16 and √25The prime factorization method is used to write a square root of a non-perfect square number in the simplest radical form.

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.?

Solution:

We know, each side of square = AreaWe will use the same concept to find the dimension of each tile.Area of bathroom = the area of 20tiles, which is given as 340 square inches.Area of each tile = 340÷20 = 17 square inchesLength of each side of tile = √17= 4.1231 inches


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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.

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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.