Square Root of 3400
The square root of 3400 is expressed as √3400 in the radical form and as (3400)½ or (3400)0.5 in the exponent form. The square root of 3400 rounded up to 9 decimal places is 58.309518948. It is the positive solution of the equation x2 = 3400. We can express the square root of 3400 in its lowest radical form as 10 √34.
- Square Root of 3400: 58.309518948453004
- Square Root of 3400 in exponential form: (3400)½ or (3400)0.5
- Square Root of 3400 in radical form: √3400 or 10 √34
| 1. | What is the Square Root of 3400? |
| 2. | How to find the Square Root of 3400? |
| 3. | Is the Square Root of 3400 Irrational? |
| 4. | FAQs |
What is the Square Root of 3400?
The square root of 3400, (or root 3400), is the number which when multiplied by itself gives the product as 3400. Therefore, the square root of 3400 = √3400 = 10 √34 = 58.309518948453004.
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How to Find Square Root of 3400?
Value of √3400 by Long Division Method
Explanation:
- Forming pairs: 34 and 00
- Find a number Y (5) such that whose square is <= 34. Now divide 34 by 5 with quotient as 5.
- Bring down the next pair 00, to the right of the remainder 9. The new dividend is now 900.
- Add the last digit of the quotient (5) to the divisor (5) i.e. 5 + 5 = 10. To the right of 10, find a digit Z (which is 8) such that 10Z × Z <= 900. After finding Z, together 10 and Z (8) form a new divisor 108 for the new dividend 900.
- Divide 900 by 108 with the quotient as 8, giving the remainder = 900 - 108 × 8 = 900 - 864 = 36.
- Now, let's find the decimal places after the quotient 58.
- Bring down 00 to the right of this remainder 36. The new dividend is now 3600.
- Add the last digit of quotient to divisor i.e. 8 + 108 = 116. To the right of 116, find a digit Z (which is 3) such that 116Z × Z <= 3600. Together they form a new divisor (1163) for the new dividend (3600).
- Divide 3600 by 1163 with the quotient as 3, giving the remainder = 3600 - 1163 × 3 = 3600 - 3489 = 111.
- Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 3400.
Therefore, the square root of 3400 by long division method is 58.3 approximately.
Is Square Root of 3400 Irrational?
The actual value of √3400 is undetermined. The value of √3400 up to 25 decimal places is 58.30951894845300470874153. Hence, the square root of 3400 is an irrational number.
☛ Also Check:
- Square Root of 900 - √900 = 30
- Square Root of 1024 - √1024 = 32
- Square Root of 192 - √192 = 13.85641
- Square Root of 52 - √52 = 7.21110
- Square Root of 125 - √125 = 11.18034
- Square Root of 34 - √34 = 5.83095
- Square Root of 108 - √108 = 10.39230
FAQs on the Square Root of 3400
What is the Value of the Square Root of 3400?
The square root of 3400 is 58.30951.
Why is the Square Root of 3400 an Irrational Number?
Upon prime factorizing 3400 i.e. 23 × 52 × 171, 2 is in odd power. Therefore, the square root of 3400 is irrational.
If the Square Root of 3400 is 58.310. Find the Value of the Square Root of 34.
Let us represent √34 in p/q form i.e. √(3400/100) = 34/10 = 5.831. Hence, the value of √34.0 = 5.831
What is the Value of 3 square root 3400?
The square root of 3400 is 58.310. Therefore, 3 √3400 = 3 × 58.310 = 174.929.
Evaluate 5 plus 12 square root 3400
The given expression is 5 + 12 √3400. We know that the square root of 3400 is 58.310. Therefore, 5 + 12 √3400 = 5 + 12 × 58.310 = 5 + 699.714 = 704.714
What is the Square Root of 3400 in Simplest Radical Form?
We need to express 3400 as the product of its prime factors i.e. 3400 = 2 × 2 × 2 × 5 × 5 × 17. Therefore, √3400 = √2 × 2 × 2 × 5 × 5 × 17 = 10 √34. Thus, the square root of 3400 in the lowest radical form is 10 √34.