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. | IsSquare 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 thatthere does not exist any integer whose square is 34. But we can findthe square root of 34 using a calculator as√34= 5.830951894845300... To check this answer, find (5.830951894845300)2and we can see that we get 33.999... which is very close to 34.
Is the Square Root of 34Rational orIrrational?
A rational number is a number which is:
- either terminating
- or non-terminating and has a repeatingpattern 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 nota 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 factorizationof 34 is34 = 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 34by 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 boxessuch thatthe 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.
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
- Square Root of 35
- Square Root of 17
- Square Root of 68
- Square Root of 29
- Square Root of 30
Important Notes:
- 34 lies between 25 and 36. So √34 lies between √25and√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 34square feet. What is the length of herbathroom?
Solution
Let us assume that the length of the bathroom is xfeet. Then the area of the bathroom's floor is x2square feet.
By the given information:
x2= 34
x = √34= 5.83feetExample 2:Patrick prepared a pizza of area 34πsquare inches. Find its radius. Round the answer to the nearest integer.
Solution
Let us assume that the radius of the pizza is rinches. Then its area using the formula of area of a circle is πr2square 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 androunding the answer to the nearest integer,
Hence, the radius of pizza = 5.83inches
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.
Show Solution
go to slidego to slidego to slide
How can your child master math concepts?
Math mastery comes with practice and understanding the ‘Why’ behind the ‘What.’ Experience the Cuemath difference.
Book a Free Trial Class
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
