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Square Root of 34

The square root of 34 is expressed as √34 in the radical form and as (34)^½ or (34)^0.5 in the exponent form. 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

1.	What Is the Square Root of 34?
2.	Is Square Root of 34 Rational or Irrational?
3.	How to Find the Square Root of 34?
4.	Important Notes
5.	Thinking Out of the Box!
6.	FAQs on Square Root of 34

What Is the Square Root of 34?

By trial and error method, we can see that there does not exist any integer whose square is 34. But we can find the square root of 34 using a calculator as √34 = 5.830951894845300... To check this answer, find (5.830951894845300)² and we can see that we get 33.999... which is very close 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 part

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

Clearly, this is non-terminating and the decimal part has no repeating pattern. So it is not a rational number.

Thus, √34 is an irrational number.

How to Find 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 want to learn more about each of these methods, click here.

Simplified Radical Form of Square Root of 34

The prime factorization of 34 is 34 = 2 × 17

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

Square Root of 34 by Long Division Method

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

The long division process of finding the square root is not the same as the normal long division.

Step 1: In this step, we take 34 as a pair (by placing a bar over it). (If the number has an odd number of digits, then we place a bar just on the first digit; if the number has an even number of digits, then we place a bar on the first two digits together).
Step 2: Find a number whose square is very close to 34 and less than or equal to 34. We know that 5² = 25. So 5 is such a number. We write it in the place of both the quotient and the divisor.
Step 3: Since we do not have any other digits of 34 to carry forward, we write pairs of zeros after the decimal point (as 34 = 34.000000...). We write as many pairs as we want the number of decimals after the decimal point in the final result. Let us calculate √34 up to 3 decimals. So we write 3 pairs of zeros. Since we have taken a decimal point in the dividend, let us write a decimal point in the quotient as well after 5.
Step 4: Remember that we always carry forward two digits at a time while finding a square root. So we carry forward two zeros at a time. Double the quotient and write it as the divisor of the next division. But note that this is not the complete divisor.
Step 5: Now a part of the divisor is 10; think which number should replace each of the boxes such that the product is very close to 900 and is less than or equal to 900. We have 108 × 8 = 864. Thus, the required number is 8. Include it in both the divisor and quotient.
Step 6: We repeat step 3 and step 4 for the corresponding divisors and quotients of the subsequent divisions.

Square Root of 34 by Long Division

So far we have got √34 = 5.830

If we repeat this process further, we get, √34 = 5.830951894845300...

Explore Square roots using illustrations and interactive examples

Important Notes:

34 lies between 25 and 36. So √34 lies between √25 and √36.That is, √34 lies between 5 and 6.
The prime factorization method is used to write a square root of a non-perfect square number in the simplest radical form. For example: 45 = 3 × 3 × 5 = 3² × 3⁵. So, √45 = √3² × √5 = 3√5.

Think Tank:

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

Square Root of 34 Solved Examples

Example 1: Harper wants to cover her bathroom floor with tiles. The floor is square-shaped and it has an area of 34 square feet. What is the length of her bathroom?

Solution

Let us assume that the length of the bathroom is x feet. Then the area of the bathroom's floor is x² square feet.

By the given information:

x²= 34
x = √34 = 5.83 feet
Example 2: Patrick prepared a pizza of area 34π square inches. Find its radius. Round the answer to the nearest integer.

Solution

Let us assume that the radius of the pizza is r inches. Then its area using the formula of area of a circle is πr² square inches. By the given information, πr² = 34π

r² = 34

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

Hence, the radius of pizza = 5.83 inches
Example: Solve the equation x² − 34 = 0

Solution:

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

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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 Square Root of 34 an Irrational Number?

Upon prime factorizing 34 i.e. 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 = 9 × 5.831 = 52.479.

If the Square Root of 34 is 5.831. Find the Value of the Square Root of 0.34.

Let 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 express 34 as the product of its prime factors i.e. 34 = 2 × 17. Therefore, as visible, the radical form of the square root of 34 cannot be simplified further. Therefore, the simplest radical form of the square root of 34 can be written as √34

Evaluate 19 plus 11 square root 34

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

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