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.

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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

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Value of √3400 by Long Division Method

Explanation:

Forming pairs: 34 and 00Find a number Y (5) such that whose square is 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 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 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.


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Example 1: Solve the equation x2 − 3400 = 0

Solution:

x2 - 3400 = 0 i.e. x2 = 3400x = ±√3400Since the value of the square root of 3400 is 58.310,⇒ x = +√3400 or -√3400 = 58.310 or -58.310.


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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.

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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.