Is 34 A Rational Number

Foursquare Root of 34

The square root of 34 is expressed as √34 in the radical form and equally (34)^½ or (34)^0.5 in the exponent course. The square root of 34 rounded up to 8 decimal places is 5.83095189. It is the positive solution of the equation x² = 34.

Square Root of 34: 5.830951894845301
Square Root of 34 in exponential form: (34)^½ or (34)^0.5
Square Root of 34 in radical form: √34

one.	What Is the Square Root of 34?
2.	Is Square Root of 34 Rational or Irrational?
three.	How to Find the Square Root of 34?
four.	Important Notes
5.	Thinking Out of the Box!
half dozen.	FAQs on Square Root of 34

What Is the Foursquare Root of 34?

By trial and error method, nosotros tin can meet that there does not exist any integer whose square is 34. Merely nosotros can discover the square root of 34 using a calculator as√34 = five.830951894845300... To check this respond, find (five.830951894845300)² and we tin can meet that we get 33.999... which is very shut to 34.

Is the Square Root of 34 Rational or Irrational?

A rational number is a number which is:

either terminating
or non-terminating and has a repeating pattern in its decimal role

In the previous section, we saw that: √34 =5.830951894845300...

Clearly, this is non-terminating and the decimal office has no repeating pattern. Then information technology is not a rational number.

Thus,√34 is an irrational number.

How to Discover the Square Root of 34?

We can find the square root of 34 using various methods.

Repeated Subtraction
Prime Factorization
Estimation and Approximation
Long Division

If you lot want to acquire more than about each of these methods, click hither.

Simplified Radical Form of Square Root of 34

The prime factorization of 34 is 34 = 2 × 17

To find the square root of whatsoever number, we have one number from each pair consisting of same numbers and we multiply them. But the prime number factorization of 34 is 2 × 17, which has no pairs consisting of same numbers. Thus,√34 cannot exist simplified whatsoever further.

Square Root of 34 by Long Partitioning Method

The square root of 34 can be found using the long division as follows.

The long division procedure of finding the square root is not the same equally the normal long division.

Footstep i: In this pace, we take 34 as a pair (past placing a bar over it). (If the number has an odd number of digits, and so we place a bar just on the beginning digit; if the number has an even number of digits, then we identify a bar on the starting time 2 digits together).
Footstep 2:Find a number whose square is very shut to 34 and less than or equal to 34. Nosotros know that 5² = 25. So five is such a number. We write information technology in the identify of both the quotient and the divisor.
Step 3: Since we do not have whatever other digits of 34 to conduct forward, we write pairs of zeros after the decimal betoken (equally 34 = 34.000000...). We write every bit many pairs as we want the number of decimals after the decimal point in the concluding result. Let us summate √34 upwardly to three decimals. So nosotros write 3 pairs of zeros. Since nosotros accept taken a decimal point in the dividend, let us write a decimal point in the quotient every bit well after v.
Step 4: Remember that we always carry forward 2 digits at a time while finding a square root. So we carry forward two zeros at a time. Double the quotient and write information technology as the divisor of the adjacent division. But note that this is not the consummate divisor.
Step five: At present a role of the divisor is ten; think which number should supervene upon each of the boxes such that the product is very close to 900 and is less than or equal to 900. We have 108 × viii = 864. Thus, the required number is eight. Include it in both the divisor and quotient.
Step half dozen: We repeat stride three and step iv for the corresponding divisors and quotients of the subsequent divisions.

Square Root of 34 by Long Division

So far nosotros have got √34 = 5.830

If nosotros repeat this procedure further, we become,√34 = 5.830951894845300...

Explore Square roots using illustrations and interactive examples

Square Root of 35
Square Root of 17
Square Root of 68
Foursquare Root of 29
Square Root of 30

Important Notes:

34 lies between 25 and 36. So √34 lies between √25 and√36.That is, √34 lies between 5 and vi.
The prime factorization method is used to write a square root of a non-perfect square number in the simplest radical form. For case: 45 = three × 3 × 5 = 3² × three⁵. And then, √45 = √3² × √five = three√5.

Retrieve Tank:

Can the value of a foursquare root be negative as well? Hint: Think what is the foursquare of a negative number.
Is √-34 a real number?Hint: Recollect whether there is any real number whose foursquare is negative.

Square Root of 34 Solved Examples

Instance 1: Harper wants to cover her bath floor with tiles. The floor is square-shaped and it has an surface area of 34 square anxiety. What is the length of her bath?

Solution

Let united states assume that the length of the bath is x feet. Then the area of the bathroom'southward floor is x^two square feet.

By the given information:

x²= 34
x = √34 = 5.83 feet
Example two: Patrick prepared a pizza of area 34π square inches. Find its radius. Circular the reply to the nearest integer.

Solution

Permit us assume that the radius of the pizza is r inches. And so its area using the formula of expanse of a circumvolve is πr² square inches. By the given information, πr^two = 34π

r² = 34

By taking the square root on both sides, √r² =√34. We know that the square root of r²is r. Past calculating the square root of 34 and rounding the reply to the nearest integer,

Hence, the radius of pizza = v.83 inches
Example: Solve the equation ten^two − 34 = 0

Solution:

x² - 34 = 0 i.e. tenⁱⁱ = 34
x = ±√34
Since the value of the square root of 34 is 5.831,
⇒ x = +√34 or -√34 = 5.831 or -five.831.

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FAQs on the Square Root of 34

What is the Value of the Square Root of 34?

The square root of 34 is 5.83095.

Why is the Foursquare Root of 34 an Irrational Number?

Upon prime factorizing 34 i.due east. 2¹ × 17¹, 2 is in odd power. Therefore, the square root of 34 is irrational.

What is the Value of 9 square root 34?

The square root of 34 is 5.831. Therefore, 9 √34 = ix × five.831 = 52.479.

If the Foursquare Root of 34 is 5.831. Notice the Value of the Foursquare Root of 0.34.

Permit us represent √0.34 in p/q form i.e. √(34/100) = 0.34/10 = 0.583. Hence, the value of √0.34 = 0.583

What is the Square Root of 34 in Simplest Radical Form?

We need to limited 34 as the product of its prime factors i.e. 34 = two × 17. Therefore, as visible, the radical class of the foursquare root of 34 cannot be simplified farther. Therefore, the simplest radical grade of the foursquare root of 34 can be written as √34

Evaluate xix plus 11 square root 34

The given expression is xix + eleven √34. We know that the square root of 34 is v.831. Therefore, xix + eleven √34 = nineteen + 11 × 5.831 = 19 + 64.140 = 83.140